Pub Date : 2025-04-01DOI: 10.1016/S0034-4877(25)00022-9
Shahroud Azami
In this paper, we consider the Lie groups ℍ2 × ℝ and Sol3 with left-invariant Riemannian metrics and we study the Riemann solitons on them. We prove that the Lie group ℍ2 × ℝ admits the Riemann soliton and the Lie group Sol3 does not admit the Riemann soliton. We classify all Riemann solitons on the Lie group ℍ2 × ℝ and we show which of the potential vector fields of Riemann solitons are Killing, Ricci collineation, and Ricci bi-conformal vector fields. Also, we classify all Ricci bi-conformal vector fields on the Lie group Sol3 and we show which of them are Killing and Ricci collineation.
{"title":"Riemann Solitons on ℍ2 × ℝ and Sol3","authors":"Shahroud Azami","doi":"10.1016/S0034-4877(25)00022-9","DOIUrl":"10.1016/S0034-4877(25)00022-9","url":null,"abstract":"<div><div>In this paper, we consider the Lie groups <strong>&</strong>Hopf;<sup>2</sup> × ℝ and Sol<sub>3</sub> with left-invariant Riemannian metrics and we study the Riemann solitons on them. We prove that the Lie group <strong>&</strong>Hopf;<sup>2</sup> × ℝ admits the Riemann soliton and the Lie group Sol<sub>3</sub> does not admit the Riemann soliton. We classify all Riemann solitons on the Lie group <strong>&</strong>Hopf;<sup>2</sup> × ℝ and we show which of the potential vector fields of Riemann solitons are Killing, Ricci collineation, and Ricci bi-conformal vector fields. Also, we classify all Ricci bi-conformal vector fields on the Lie group Sol<sub>3</sub> and we show which of them are Killing and Ricci collineation.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 2","pages":"Pages 141-154"},"PeriodicalIF":1.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-01DOI: 10.1016/S0034-4877(25)00025-4
UMME ZAINAB
In this article, the family of Sheffer-associated λ polynomials is introduced, and their quasi-monomial properties are established. Additionally, certain properties of these polynomials are explored using umbral algebraic matrix algebra. This approach provides a powerful tool for investigating the properties of multi-variable special polynomials. The recursive formulae and differential equations for these polynomials are derived using the properties and relationships between the Pascal functional and Wronskian matrices. The corresponding results for the Appellassociated λ polynomials and Appell-λ polynomial families are also obtained. Furthermore, these findings are demonstrated for the Hermite-λ, exponential-λ, and Miller-Lee-λ polynomials.
{"title":"THE UMBRAL-ALGEBRAIC APPROACH TO STUDY THE SHEFFER-λ POLYNOMIALS","authors":"UMME ZAINAB","doi":"10.1016/S0034-4877(25)00025-4","DOIUrl":"10.1016/S0034-4877(25)00025-4","url":null,"abstract":"<div><div>In this article, the family of Sheffer-associated λ polynomials is introduced, and their quasi-monomial properties are established. Additionally, certain properties of these polynomials are explored using umbral algebraic matrix algebra. This approach provides a powerful tool for investigating the properties of multi-variable special polynomials. The recursive formulae and differential equations for these polynomials are derived using the properties and relationships between the Pascal functional and Wronskian matrices. The corresponding results for the Appellassociated λ polynomials and Appell-λ polynomial families are also obtained. Furthermore, these findings are demonstrated for the Hermite-λ, exponential-λ, and Miller-Lee-λ polynomials.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 2","pages":"Pages 215-240"},"PeriodicalIF":1.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-01DOI: 10.1016/S0034-4877(25)00021-7
Cheng Da , Hony-Yi Fan
Partition function is an important physical quantity and is related to various thermodynamic functions, also is a key link that connects microscopic and macroscopic physical phenomena. In this article for the first time we calculate partition function Tr exp {-iβt γj,b γj+1,a) for 1-dimensional Kitaev chain model which engenders the Majorana zero mode (MZM), where are Dirac fermionic annihilation and creation operators. Following Fan's theorem we successfully disentangle exp {-iβt γj,b γj+1,a) and derive the partition function by using the fermionic coherent state representation.
{"title":"Partition Function for 1-Dimensional Kitaev Chain Model Engendering the Majorana Zero Mode","authors":"Cheng Da , Hony-Yi Fan","doi":"10.1016/S0034-4877(25)00021-7","DOIUrl":"10.1016/S0034-4877(25)00021-7","url":null,"abstract":"<div><div>Partition function is an important physical quantity and is related to various thermodynamic functions, also is a key link that connects microscopic and macroscopic physical phenomena. In this article for the first time we calculate partition function Tr exp {-<em>iβt γ<sub>j,b</sub> γ<sub>j</sub></em>+1,<em><sub>a</sub></em>) for 1-dimensional Kitaev chain model which engenders the Majorana zero mode (MZM), where \u0000\t\t\t\t<span><math><mrow><msub><mi>y</mi><mrow><mi>j</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>a</mi></mrow></msub><mo>=</mo><msubsup><mi>c</mi><mrow><mi>j</mi><mo>+</mo><mn>1</mn></mrow><mo>†</mo></msubsup><mo>+</mo><msub><mi>c</mi><mrow><mi>j</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>y</mi><mrow><mi>j</mi><mo>,</mo><mi>b</mi></mrow></msub><mo>=</mo><mrow><mo>(</mo><mrow><msub><mi>c</mi><mi>j</mi></msub><mo>-</mo><msubsup><mi>c</mi><mi>j</mi><mo>†</mo></msubsup></mrow><mo>)</mo></mrow><mo>/</mo><mi>i</mi><mo>,</mo><mrow><mo>(</mo><mrow><msub><mi>c</mi><mrow><mi>j</mi><mo>,</mo></mrow></msub><msubsup><mi>c</mi><mi>j</mi><mo>†</mo></msubsup></mrow><mo>)</mo></mrow></mrow></math></span> are Dirac fermionic annihilation and creation operators. Following Fan's theorem we successfully disentangle exp {-<em>iβt γ<sub>j,b</sub> γ<sub>j</sub></em>+1,<em><sub>a</sub></em>) and derive the partition function by using the fermionic coherent state representation.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 2","pages":"Pages 129-140"},"PeriodicalIF":1.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-01DOI: 10.1016/S0034-4877(25)00026-6
JUAN BORY-REYES , DIANA BARSEGHYAN, BARUCH SCHNEIDER
In this present paper we consider the asymptotically Archimedean spiral-shaped regions for which the Dirichlet Laplacian spectrum consists of the essential part and the eigenvalues below the threshold of the essential spectrum. Our purpose here is to obtain the bounds on the moments of these eigenvalues in terms of the geometric properties of the region. As a consequence of the mentioned bound we describe the class of the asymptotically Archimedean spiral-shaped regions such that the Dirichlet Laplacian has only a finite number of eigenvalues below the threshold of the essential spectrum.
{"title":"LIEB–THIRRING TYPE ESTIMATES FOR DIRICHLET LAPLACIANS ON SPIRAL-SHAPED DOMAINS","authors":"JUAN BORY-REYES , DIANA BARSEGHYAN, BARUCH SCHNEIDER","doi":"10.1016/S0034-4877(25)00026-6","DOIUrl":"10.1016/S0034-4877(25)00026-6","url":null,"abstract":"<div><div>In this present paper we consider the asymptotically Archimedean spiral-shaped regions for which the Dirichlet Laplacian spectrum consists of the essential part and the eigenvalues below the threshold of the essential spectrum. Our purpose here is to obtain the bounds on the moments of these eigenvalues in terms of the geometric properties of the region. As a consequence of the mentioned bound we describe the class of the asymptotically Archimedean spiral-shaped regions such that the Dirichlet Laplacian has only a finite number of eigenvalues below the threshold of the essential spectrum.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 2","pages":"Pages 241-257"},"PeriodicalIF":1.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-01DOI: 10.1016/S0034-4877(25)00023-0
PATRICK ERIK BRADLEY, ÁNGEL MORÁN LEDEZMA
Motivated by the recently proven presence of ultrametricity in physical models (certain spin glasses), the very recent study of Turing patterns on locally ultrametric state spaces, and the study of Turing patterns in time changing networks, first nonautonomous diffusion operators on such systems, where finitely many compact p-adic spaces are joined by a graph structure, are studied, including their Dirichlet and von Neumann eigenvalues. Secondly, the Cauchy problem for the heat equation associated with these operators is solved, its solution approximated by Trotter products, and thirdly, the corresponding Feller property as well as the Markov property (a Hunt process) is established.
{"title":"A NONAUTONOMOUS p-ADIC DIFFUSION EQUATION ON TIME CHANGING GRAPHS","authors":"PATRICK ERIK BRADLEY, ÁNGEL MORÁN LEDEZMA","doi":"10.1016/S0034-4877(25)00023-0","DOIUrl":"10.1016/S0034-4877(25)00023-0","url":null,"abstract":"<div><div>Motivated by the recently proven presence of ultrametricity in physical models (certain spin glasses), the very recent study of Turing patterns on locally ultrametric state spaces, and the study of Turing patterns in time changing networks, first nonautonomous diffusion operators on such systems, where finitely many compact <em>p</em>-adic spaces are joined by a graph structure, are studied, including their Dirichlet and von Neumann eigenvalues. Secondly, the Cauchy problem for the heat equation associated with these operators is solved, its solution approximated by Trotter products, and thirdly, the corresponding Feller property as well as the Markov property (a Hunt process) is established.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 2","pages":"Pages 155-180"},"PeriodicalIF":1.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-04-01DOI: 10.1016/S0034-4877(25)00024-2
Andrzej Krasiński
The maximally extended Reissner-Nordström (RN) spacetime with e2m2 can be interpreted either as an infinite chain of asymptotically flat regions connected by tunnels between timelike singularities or as a set of just one pair of asymptotically flat regions and one tunnel; the repetitions of this set in the infinite chain being identified. The second interpretation gives rise to the suspicion of acausality, i.e. the possibility of sending messages to one’s own past. A numerical investigation of this problem was carried out in this paper and gave the following result. Let E be the initial point of a radial timelike future-directed ingoing geodesic G, lying halfway between the outer horizon and the image of the null infinity in the maximally extended RN spacetime. Let E’ be the first future copy of E. It was verified whether the turning point of G lies outside or inside the past light cone (PLC) of E′. In the second case the breach of causality does occur. It turned out that the acausality is present when VE, the timelike coordinate of E, is negative with a sufficiently large |VE|, and is absent with a sufficiently large VE > 0. In between these values there exists a , dependent on the initial data for the geodesic, for which the turning point lies on the PLC. So, the identification does lead to acausality. Nonradial timelike and null geodesics were also investigated, and a few hitherto unknown properties of the maximal extension were revealed. For example, the singularity arc at r = 0 may be convex or concave, depending on the values of m and e.
{"title":"Causality in the Maximally Extended Reissner-NordstrÖm Spacetime With Identifications","authors":"Andrzej Krasiński","doi":"10.1016/S0034-4877(25)00024-2","DOIUrl":"10.1016/S0034-4877(25)00024-2","url":null,"abstract":"<div><div>The maximally extended Reissner-Nordström (RN) spacetime with <em>e</em><sup>2</sup> <em>m</em><sup>2</sup> can be interpreted either as an infinite chain of asymptotically flat regions connected by tunnels between timelike singularities or as a set of just one pair of asymptotically flat regions and one tunnel; the repetitions of this set in the infinite chain being identified. The second interpretation gives rise to the suspicion of acausality, i.e. the possibility of sending messages to one’s own past. A numerical investigation of this problem was carried out in this paper and gave the following result. Let E be the initial point of a radial timelike future-directed ingoing geodesic G, lying halfway between the outer horizon and the image of the null infinity in the maximally extended RN spacetime. Let E’ be the first future copy of E. It was verified whether the turning point of G lies outside or inside the past light cone (PLC) of E′. In the second case the breach of causality does occur. It turned out that the acausality is present when <em>V<sub>E</sub></em>, the timelike coordinate of E, is negative with a sufficiently large |<em>V<sub>E</sub></em>|, and is absent with a sufficiently large <em>V<sub>E</sub></em> > 0. In between these values there exists a \u0000\t\t\t\t<span><math><mrow><msub><mover><mi>V</mi><mo>~</mo></mover><mi>E</mi></msub></mrow></math></span>, dependent on the initial data for the geodesic, for which the turning point lies on the PLC. So, the identification does lead to acausality. Nonradial timelike and null geodesics were also investigated, and a few hitherto unknown properties of the maximal extension were revealed. For example, the singularity arc at <em>r</em> = 0 may be convex or concave, depending on the values of <em>m</em> and <em>e</em>.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 2","pages":"Pages 181-214"},"PeriodicalIF":1.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/S0034-4877(25)00009-6
Hülya Bağdatli Yilmaz, Uday Chand De
This paper aims at investigating pseudo Z symmetric space-times (PZS)4 admitting a type of semi-symmetric nonmetric connection (ssnmc). At first, we scrutinize the impact of a ssnmc on Lorentzian manifolds and establish a nontrivial example. Then, we examine the general properties of (PZS)4 space-times and express the physical consequences of this space-time. Among others, it is demonstrated that a (PZS)4 space-time admitting a ssnmc whose Ricci tensor vanishes becomes a GRW space-time as well as a perfect fluid space-time and a purely electric space-time under a certain condition.
{"title":"Pseudo Z Symmetric Space-Times Admitting a Type of Semi-Symmetric Nonmetric Connection","authors":"Hülya Bağdatli Yilmaz, Uday Chand De","doi":"10.1016/S0034-4877(25)00009-6","DOIUrl":"10.1016/S0034-4877(25)00009-6","url":null,"abstract":"<div><div>This paper aims at investigating pseudo Z symmetric space-times (PZS)<sub>4</sub> admitting a type of semi-symmetric nonmetric connection (ssnmc). At first, we scrutinize the impact of a ssnmc on Lorentzian manifolds and establish a nontrivial example. Then, we examine the general properties of (PZS)<sub>4</sub> space-times and express the physical consequences of this space-time. Among others, it is demonstrated that a (PZS)<sub>4</sub> space-time admitting a ssnmc whose Ricci tensor vanishes becomes a GRW space-time as well as a perfect fluid space-time and a purely electric space-time under a certain condition.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 1","pages":"Pages 39-52"},"PeriodicalIF":1.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/S0034-4877(25)00008-4
Koushik Ray, Siddhartha Sen
In this paper topological K-group calculations for fiber bundles with structure group SO(3) over tori are carried out to explain why topological insulators have special conducting points on their surface but are bulk insulators. It is shown that these special points are gapless and conducting for topological reasons and follow from the K-group calculations. The existence of gapless surface points is established with the help of an additional topological property of the K-groups which relates them to the index theorem of an operator. The index theorem relates zeros of operators to topology. For the topological insulator the relevant operator is a Dirac operator, that emerges in the problem because the system has strong spin-orbit interactions and time reversal invariance. Calculating K-groups over tori require some special topological tools that are not widely known. These are explained. We then show that the actual calculation of K-groups over tori becomes straightforward once a few topological results are in place. Since condensed matter systems with periodic lattices are always bundles over tori the procedures described is of general interest.
{"title":"Topology behind Topological Insulators","authors":"Koushik Ray, Siddhartha Sen","doi":"10.1016/S0034-4877(25)00008-4","DOIUrl":"10.1016/S0034-4877(25)00008-4","url":null,"abstract":"<div><div>In this paper topological <em>K</em>-group calculations for fiber bundles with structure group SO(3) over tori are carried out to explain why topological insulators have special conducting points on their surface but are bulk insulators. It is shown that these special points are gapless and conducting for topological reasons and follow from the <em>K</em>-group calculations. The existence of gapless surface points is established with the help of an additional topological property of the <em>K</em>-groups which relates them to the index theorem of an operator. The index theorem relates zeros of operators to topology. For the topological insulator the relevant operator is a Dirac operator, that emerges in the problem because the system has strong spin-orbit interactions and time reversal invariance. Calculating <em>K</em>-groups over tori require some special topological tools that are not widely known. These are explained. We then show that the actual calculation of <em>K</em>-groups over tori becomes straightforward once a few topological results are in place. Since condensed matter systems with periodic lattices are always bundles over tori the procedures described is of general interest.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 1","pages":"Pages 11-37"},"PeriodicalIF":1.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/S0034-4877(25)00012-6
Muzaffar M. Rahmatullaev, Zulxumor T. Abdukaxorova
In the present paper, we investigate weakly periodic p-adic generalized Gibbs measures for p-adic Ising model with an external field on the Cayley tree of order two. For a normal subgroup of the group representation of the Cayley tree we prove that there exists at least one unbounded weakly periodic (in particular, nonperiodic) p-adic generalized Gibbs measures for this model. Moreover, we show that if p is any odd prime then a phase transition occurs, if p = 2 then a quasi phase transition occurs for p-adic Ising model with an external field.
{"title":"On HA-Weakly Periodic P-Adic Generalized Gibbs Measures of P-Adic Ising Model with an External Field on a Cayley Tree","authors":"Muzaffar M. Rahmatullaev, Zulxumor T. Abdukaxorova","doi":"10.1016/S0034-4877(25)00012-6","DOIUrl":"10.1016/S0034-4877(25)00012-6","url":null,"abstract":"<div><div>In the present paper, we investigate weakly periodic <em>p</em>-adic generalized Gibbs measures for <em>p</em>-adic Ising model with an external field on the Cayley tree of order two. For a normal subgroup of the group representation of the Cayley tree we prove that there exists at least one unbounded weakly periodic (in particular, nonperiodic) <em>p</em>-adic generalized Gibbs measures for this model. Moreover, we show that if <em>p</em> is any odd prime then a phase transition occurs, if <em>p</em> = 2 then a quasi phase transition occurs for <em>p</em>-adic Ising model with an external field.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 1","pages":"Pages 93-109"},"PeriodicalIF":1.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/S0034-4877(25)00013-8
Hyelim Han
In this article, we study the variational problem of maximizing a certain linear combination of area functionals of a closed generalized linear Weingarten spacelike hypersurface Mn immersed in a foliated spacetime . Given a Robertson-Walker spacetime , we exhibit conditions on Mn which guarantee that (strong) stability is necessary and sufficient for Mn to be totally umbilic. Under a suitable restriction on Mn, we also prove that if a closed generalized linear Weingarten spacelike hypersurface in is (strongly) stable, then it must be a totally umbilic round sphere.
{"title":"Stability of a Generalized Linear Weingarten Spacelike Hypersurface in Robertson–Walker Spacetimes","authors":"Hyelim Han","doi":"10.1016/S0034-4877(25)00013-8","DOIUrl":"10.1016/S0034-4877(25)00013-8","url":null,"abstract":"<div><div>In this article, we study the variational problem of maximizing a certain linear combination of area functionals of a closed generalized linear Weingarten spacelike hypersurface <em>M<sup>n</sup></em> immersed in a foliated spacetime \u0000\t\t\t\t<span><math><mrow><msubsup><mover><mi>M</mi><mo>~</mo></mover><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msubsup></mrow></math></span>. Given a Robertson-Walker spacetime \u0000\t\t\t\t<span><math><mrow><msubsup><mover><mi>M</mi><mo>~</mo></mover><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msubsup><mrow><mo>(</mo><mi>c</mi><mo>)</mo></mrow><mo>=</mo><mi>I</mi><msub><mo>×</mo><mi>ϕ</mi></msub><msup><mi>F</mi><mi>n</mi></msup></mrow></math></span>, we exhibit conditions on <em>M<sup>n</sup></em> which guarantee that (strong) stability is necessary and sufficient for <em>M<sup>n</sup></em> to be totally umbilic. Under a suitable restriction on <em>M<sup>n</sup></em>, we also prove that if a closed generalized linear Weingarten spacelike hypersurface in \u0000\t\t\t\t<span><math><mrow><msubsup><mi>S</mi><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msubsup></mrow></math></span> is (strongly) stable, then it must be a totally umbilic round sphere.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 1","pages":"Pages 111-128"},"PeriodicalIF":1.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号