Pub Date : 2024-06-20DOI: 10.1016/j.difgeo.2024.102166
Charles P. Boyer , Christina W. Tønnesen-Friedman
In a previous paper [18] the authors employed the fiber join construction of Yamazaki [38] together with the admissible construction of Apostolov, Calderbank, Gauduchon, and Tønnesen-Friedman [2] to construct new extremal Sasaki metrics on odd dimensional sphere bundles over smooth projective algebraic varieties. In the present paper we continue this study by applying a recent existence theorem [14] that shows that under certain conditions one can always obtain a constant scalar curvature Sasaki metric in the Sasaki cone. Moreover, we explicitly describe this construction for certain sphere bundles of dimension 5 and 7.
{"title":"Sasakian geometry on sphere bundles II: Constant scalar curvature","authors":"Charles P. Boyer , Christina W. Tønnesen-Friedman","doi":"10.1016/j.difgeo.2024.102166","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102166","url":null,"abstract":"<div><p>In a previous paper <span>[18]</span> the authors employed the fiber join construction of Yamazaki <span>[38]</span> together with the admissible construction of Apostolov, Calderbank, Gauduchon, and Tønnesen-Friedman <span>[2]</span> to construct new extremal Sasaki metrics on odd dimensional sphere bundles over smooth projective algebraic varieties. In the present paper we continue this study by applying a recent existence theorem <span>[14]</span> that shows that under certain conditions one can always obtain a constant scalar curvature Sasaki metric in the Sasaki cone. Moreover, we explicitly describe this construction for certain sphere bundles of dimension 5 and 7.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"96 ","pages":"Article 102166"},"PeriodicalIF":0.6,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141434496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-30DOI: 10.1016/j.difgeo.2024.102153
Miguel Ortega , Handan Yıldırım
In this paper, we deal with non-degenerate translators of the mean curvature flow in the well-known Einstein's static universe. We focus on the rotationally invariant translators, that is, those invariant by a natural isometric action of the special orthogonal group on the ambient space. In the classification list, there are three space-like cases and five time-like cases. All of them, except a totally geodesic example, have one or two conic singularities. Also, we show a uniqueness result based on the behaviour of the translator on its boundary. As an application, we extend an isometry of the sphere to the whole translator under simple conditions. This leads to a characterization of a bowl-like example.
{"title":"Rotationally invariant translators of the mean curvature flow in Einstein's static universe","authors":"Miguel Ortega , Handan Yıldırım","doi":"10.1016/j.difgeo.2024.102153","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102153","url":null,"abstract":"<div><p>In this paper, we deal with non-degenerate translators of the mean curvature flow in the well-known Einstein's static universe. We focus on the rotationally invariant translators, that is, those invariant by a natural isometric action of the special orthogonal group on the ambient space. In the classification list, there are three space-like cases and five time-like cases. All of them, except a totally geodesic example, have one or two conic singularities. Also, we show a uniqueness result based on the behaviour of the translator on its boundary. As an application, we extend an isometry of the sphere to the whole translator under simple conditions. This leads to a characterization of a bowl-like example.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"95 ","pages":"Article 102153"},"PeriodicalIF":0.5,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0926224524000469/pdfft?md5=6bc58615dc3e4e9f74770ce03c1820e6&pid=1-s2.0-S0926224524000469-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141244155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-28DOI: 10.1016/j.difgeo.2024.102155
Dong Gao , Hui Ma , Zeke Yao
We give a complete classification of isoparametric hypersurfaces in a product space of 2-dimensional space forms for with . In fact we prove that any isoparametric hypersurface in such a space has constant product angle function, which enables us to remove the condition of constant principal curvatures from the classification obtained recently by J.B.M. dos Santos and J.P. dos Santos.
我们给出了κi∈{-1,0,1},κ1≠κ2 的二维空间形式的乘积空间 Mκ12×Mκ22 中的等参数超曲面的完整分类。事实上,我们证明了在这样的空间中任何等参数超曲面都具有恒积角函数,这使我们能够从 J.B.M. dos Santos 和 J.P. dos Santos 最近获得的分类中移除恒主曲率的条件。
{"title":"Isoparametric hypersurfaces in product spaces of space forms","authors":"Dong Gao , Hui Ma , Zeke Yao","doi":"10.1016/j.difgeo.2024.102155","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102155","url":null,"abstract":"<div><p>We give a complete classification of isoparametric hypersurfaces in a product space <span><math><msubsup><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi>κ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><mn>2</mn></mrow></msubsup><mo>×</mo><msubsup><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi>κ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mrow><mn>2</mn></mrow></msubsup></math></span> of 2-dimensional space forms for <span><math><msub><mrow><mi>κ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>∈</mo><mo>{</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></span> with <span><math><msub><mrow><mi>κ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≠</mo><msub><mrow><mi>κ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. In fact we prove that any isoparametric hypersurface in such a space has constant product angle function, which enables us to remove the condition of constant principal curvatures from the classification obtained recently by J.B.M. dos Santos and J.P. dos Santos.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"95 ","pages":"Article 102155"},"PeriodicalIF":0.5,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141244156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-23DOI: 10.1016/j.difgeo.2024.102154
Fue Zhang , Wei Zhao
The present paper is devoted to the investigation of absolutely continuous curves in asymmetric metric spaces induced by Finsler structures. Firstly, for asymmetric spaces induced by Finsler manifolds, we show that three different kinds of absolutely continuous curves coincide when their domains are bounded closed intervals. As an application, a universal existence and regularity theorem for gradient flow is obtained in the Finsler setting. Secondly, we study absolutely continuous curves in Wasserstein spaces over Finsler manifolds and establish the Lisini structure theorem in this setting, which characterize the nature of absolutely continuous curves in Wasserstein spaces in terms of dynamical transference plans concentrated on absolutely continuous curves in base Finsler manifolds. Besides, a close relation between continuity equations and absolutely continuous curves in Wasserstein spaces is founded. Last but not least, we also consider nonsmooth “Finsler-like” spaces, in which case most of the aforementioned results remain valid. Various model examples are constructed in this paper, which point out genuine differences between the asymmetric and symmetric settings.
{"title":"Absolutely continuous curves in Finsler-like spaces","authors":"Fue Zhang , Wei Zhao","doi":"10.1016/j.difgeo.2024.102154","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102154","url":null,"abstract":"<div><p>The present paper is devoted to the investigation of absolutely continuous curves in asymmetric metric spaces induced by Finsler structures. Firstly, for asymmetric spaces induced by Finsler manifolds, we show that three different kinds of absolutely continuous curves coincide when their domains are bounded closed intervals. As an application, a universal existence and regularity theorem for gradient flow is obtained in the Finsler setting. Secondly, we study absolutely continuous curves in Wasserstein spaces over Finsler manifolds and establish the Lisini structure theorem in this setting, which characterize the nature of absolutely continuous curves in Wasserstein spaces in terms of dynamical transference plans concentrated on absolutely continuous curves in base Finsler manifolds. Besides, a close relation between continuity equations and absolutely continuous curves in Wasserstein spaces is founded. Last but not least, we also consider nonsmooth “Finsler-like” spaces, in which case most of the aforementioned results remain valid. Various model examples are constructed in this paper, which point out genuine differences between the asymmetric and symmetric settings.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"96 ","pages":"Article 102154"},"PeriodicalIF":0.5,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141084325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-30DOI: 10.1016/j.difgeo.2024.102141
Inyoung Kim
We show that a compact almost-Kähler four-manifold with harmonic self-dual Weyl curvature and constant scalar curvature is Kähler if . We also prove an integral curvature inequality for compact almost-Kähler four-manifolds with harmonic self-dual Weyl curvature.
{"title":"Almost-Kähler four-manifolds with harmonic self-dual Weyl curvature","authors":"Inyoung Kim","doi":"10.1016/j.difgeo.2024.102141","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102141","url":null,"abstract":"<div><p>We show that a compact almost-Kähler four-manifold <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>ω</mi><mo>)</mo></math></span> with harmonic self-dual Weyl curvature and constant scalar curvature is Kähler if <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>⋅</mo><mo>[</mo><mi>ω</mi><mo>]</mo><mo>≥</mo><mn>0</mn></math></span>. We also prove an integral curvature inequality for compact almost-Kähler four-manifolds with harmonic self-dual Weyl curvature.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"94 ","pages":"Article 102141"},"PeriodicalIF":0.5,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140813458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-29DOI: 10.1016/j.difgeo.2024.102142
Vladimir Rovenski
Weak almost contact metric manifolds, i.e., the linear complex structure on the contact distribution is replaced by a nonsingular skew-symmetric tensor, defined by the author and R. Wolak (2022), allowed a new look at the theory of contact manifolds. This paper studies the curvature and topology of new structures of this type, called the weak nearly cosymplectic structure and weak nearly Kähler structure. We find conditions under which weak nearly cosymplectic manifolds become Riemannian products and characterize 5-dimensional weak nearly cosymplectic manifolds. Our theorems generalize results by H. Endo (2005) and A. Nicola–G. Dileo–I. Yudin (2018) to the context of weak almost contact geometry.
作者和 R. Wolak(2022 年)定义的弱近接触元流形,即接触分布上的线性复结构被非奇异偏对称张量所取代,使得接触流形理论有了新的面貌。本文研究了这类新结构的曲率和拓扑,它们被称为弱近余协结构和弱近凯勒结构。我们发现了弱近余弦流形成为黎曼积的条件,并描述了 5 维弱近余弦流形的特征。我们的定理将 H. Endo (2005) 和 A. Nicola-G. Dileo-I.Yudin (2018)在弱近接触几何背景下的结果。
{"title":"On the splitting of weak nearly cosymplectic manifolds","authors":"Vladimir Rovenski","doi":"10.1016/j.difgeo.2024.102142","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102142","url":null,"abstract":"<div><p>Weak almost contact metric manifolds, i.e., the linear complex structure on the contact distribution is replaced by a nonsingular skew-symmetric tensor, defined by the author and R. Wolak (2022), allowed a new look at the theory of contact manifolds. This paper studies the curvature and topology of new structures of this type, called the weak nearly cosymplectic structure and weak nearly Kähler structure. We find conditions under which weak nearly cosymplectic manifolds become Riemannian products and characterize 5-dimensional weak nearly cosymplectic manifolds. Our theorems generalize results by H. Endo (2005) and A. Nicola–G. Dileo–I. Yudin (2018) to the context of weak almost contact geometry.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"94 ","pages":"Article 102142"},"PeriodicalIF":0.5,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140807470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-25DOI: 10.1016/j.difgeo.2024.102143
Tian Chong , Yuxin Dong , Guilin Yang
In this paper, we investigate the stability problem of subelliptic harmonic maps with potential. First, we derive the first and second variation formulas for subelliptic harmonic maps with potential. As a result, it is proved that a subelliptic harmonic map with potential is stable if the target manifold has nonpositive curvature and the Hessian of the potential is nonpositive definite. We also give Leung type results which involve the instability of subelliptic harmonic maps with potential when the target manifold is a sphere of dimension ≥3.
{"title":"On stability of subelliptic harmonic maps with potential","authors":"Tian Chong , Yuxin Dong , Guilin Yang","doi":"10.1016/j.difgeo.2024.102143","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102143","url":null,"abstract":"<div><p>In this paper, we investigate the stability problem of subelliptic harmonic maps with potential. First, we derive the first and second variation formulas for subelliptic harmonic maps with potential. As a result, it is proved that a subelliptic harmonic map with potential is stable if the target manifold has nonpositive curvature and the Hessian of the potential is nonpositive definite. We also give Leung type results which involve the instability of subelliptic harmonic maps with potential when the target manifold is a sphere of dimension ≥3.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"94 ","pages":"Article 102143"},"PeriodicalIF":0.5,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140643595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-19DOI: 10.1016/j.difgeo.2024.102139
Ren Guan
Previously we finish the establishment of the transversality of the general part of the Vafa-Witten moduli spaces, in this paper, we deal with the rest, i.e., the reduced part. We consider Vafa-Witten equation on closed, oriented and smooth Riemann 4-manifolds with , and construct perturbation to establish the transversality of the perturbed equation. We show that for a generic choice of the perturbation terms, the moduli space of solutions to the perturbed reduced Vafa-Witten equation for the structure group or on a closed 4-manifold is a smooth manifold of dimension zero. Finally we prove that for two generic orientation-preserving parameters, the corresponding moduli spaces are cobordant, and the method can also be applied to the general part.
{"title":"Transversality of the perturbed reduced Vafa-Witten moduli spaces on 4-manifolds","authors":"Ren Guan","doi":"10.1016/j.difgeo.2024.102139","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102139","url":null,"abstract":"<div><p>Previously we finish the establishment of the transversality of the general part of the Vafa-Witten moduli spaces, in this paper, we deal with the rest, i.e., the reduced part. We consider Vafa-Witten equation on closed, oriented and smooth Riemann 4-manifolds with <span><math><mi>C</mi><mo>≡</mo><mn>0</mn></math></span>, and construct perturbation to establish the transversality of the perturbed equation. We show that for a generic choice of the perturbation terms, the moduli space of solutions to the perturbed reduced Vafa-Witten equation for the structure group <span><math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></span> or <span><math><mi>S</mi><mi>O</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></span> on a closed 4-manifold is a smooth manifold of dimension zero. Finally we prove that for two generic orientation-preserving parameters, the corresponding moduli spaces are cobordant, and the method can also be applied to the general part.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"94 ","pages":"Article 102139"},"PeriodicalIF":0.5,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140618045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-19DOI: 10.1016/j.difgeo.2024.102138
Pandeng Cao, Xiaoshu Ge, Chunping Zhong
Let be the complex Grassmann manifold and be an arbitrary -invariant strongly pseudoconvex complex Finsler metric. We prove that F is necessary a Kähler-Berwald metric which is not necessary Hermitian quadratic. We also prove that F is Hermitian quadratic if and only if F is a constant multiple of the canonical -invariant Kähler metric on . In particular on the complex projective space , there exists no -invariant strongly pseudoconvex complex Finsler metric other than a constant multiple of the Fubini-Study metric. These invariant metrics are of particular interesting since they are the most important examples of strongly pseudoconvex complex Finsler metrics on which are elliptic metrics in the sense that they enjoy very similar holomorphic sectional curvature and bisectional curvature properties as that of the -invariant Kähler metrics on , nevertheless, these invariant metrics are not necessary Hermitian quadratic, hence provide nontrivial explicit examples for complex Finsler geometry in the compact cases.
设 P:=U(p+q)/U(p)×U(q) 为复格拉斯曼流形,F:T1,0P→[0,+∞) 为任意 U(p+q)-invariant 强伪凸复 Finsler 度量。我们证明 F 是必要的 Kähler-Berwald 度量,它不是必要的赫米二次元度量。特别是在复投影空间 CPn=U(n+1)/U(n)×U(1) 上,除了 Fubini-Study 公设的常数倍之外,不存在其他 U(n+1)-invariant 强假凸复 Finsler 公设。这些不变度量特别有趣,因为它们是 P 上强伪凸复 Finsler 度量的最重要例子,而这些度量是椭圆度量,即它们享有与 P 上 U(p+q)不变 Kähler 度量非常相似的全形截面曲率和双截面曲率特性、然而,这些不变度量并不一定是赫米特四元数的,因此为紧凑情况下的复芬斯勒几何提供了非简单的明确例子。
{"title":"Characterization of invariant complex Finsler metrics on the complex Grassmann manifold","authors":"Pandeng Cao, Xiaoshu Ge, Chunping Zhong","doi":"10.1016/j.difgeo.2024.102138","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102138","url":null,"abstract":"<div><p>Let <span><math><mi>P</mi><mo>:</mo><mo>=</mo><mi>U</mi><mo>(</mo><mi>p</mi><mo>+</mo><mi>q</mi><mo>)</mo><mo>/</mo><mi>U</mi><mo>(</mo><mi>p</mi><mo>)</mo><mo>×</mo><mi>U</mi><mo>(</mo><mi>q</mi><mo>)</mo></math></span> be the complex Grassmann manifold and <span><math><mi>F</mi><mo>:</mo><msup><mrow><mi>T</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>0</mn></mrow></msup><mi>P</mi><mo>→</mo><mo>[</mo><mn>0</mn><mo>,</mo><mo>+</mo><mo>∞</mo><mo>)</mo></math></span> be an arbitrary <span><math><mi>U</mi><mo>(</mo><mi>p</mi><mo>+</mo><mi>q</mi><mo>)</mo></math></span>-invariant strongly pseudoconvex complex Finsler metric. We prove that <em>F</em> is necessary a Kähler-Berwald metric which is not necessary Hermitian quadratic. We also prove that <em>F</em> is Hermitian quadratic if and only if <em>F</em> is a constant multiple of the canonical <span><math><mi>U</mi><mo>(</mo><mi>p</mi><mo>+</mo><mi>q</mi><mo>)</mo></math></span>-invariant Kähler metric on <span><math><mi>P</mi></math></span>. In particular on the complex projective space <span><math><msup><mrow><mi>CP</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><mi>U</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>/</mo><mi>U</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>×</mo><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span>, there exists no <span><math><mi>U</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-invariant strongly pseudoconvex complex Finsler metric other than a constant multiple of the Fubini-Study metric. These invariant metrics are of particular interesting since they are the most important examples of strongly pseudoconvex complex Finsler metrics on <span><math><mi>P</mi></math></span> which are elliptic metrics in the sense that they enjoy very similar holomorphic sectional curvature and bisectional curvature properties as that of the <span><math><mi>U</mi><mo>(</mo><mi>p</mi><mo>+</mo><mi>q</mi><mo>)</mo></math></span>-invariant Kähler metrics on <span><math><mi>P</mi></math></span>, nevertheless, these invariant metrics are not necessary Hermitian quadratic, hence provide nontrivial explicit examples for complex Finsler geometry in the compact cases.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"94 ","pages":"Article 102138"},"PeriodicalIF":0.5,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140618046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-19DOI: 10.1016/j.difgeo.2024.102140
Idrees Fayaz Harry , Mehraj Ahmad Lone , Alina-Daniela Vîlcu , Gabriel-Eduard Vîlcu
This study is focused on the investigation of lightlike hypersurfaces of a generalized Robertson-Walker (GRW) spacetime. Recently, Poyraz (2022) [51], [52] established some basic inequalities involving various curvature invariants of screen homothetic lightlike hypersurfaces of GRW spacetimes, like k-scalar curvature and k-Ricci curvature. In this work, we consider other basic curvature invariants, namely the scalar curvature and δ-Casorati curvatures, and derive new inequalities for such hypersurfaces of a GRW spacetime. We also find the conditions for which the equality cases in these inequalities hold and give some applications in Lorentzian geometry.
{"title":"On some basic curvature invariants of screen homothetic lightlike hypersurfaces in a GRW spacetime","authors":"Idrees Fayaz Harry , Mehraj Ahmad Lone , Alina-Daniela Vîlcu , Gabriel-Eduard Vîlcu","doi":"10.1016/j.difgeo.2024.102140","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102140","url":null,"abstract":"<div><p>This study is focused on the investigation of lightlike hypersurfaces of a generalized Robertson-Walker (GRW) spacetime. Recently, Poyraz (2022) <span>[51]</span>, <span>[52]</span> established some basic inequalities involving various curvature invariants of screen homothetic lightlike hypersurfaces of GRW spacetimes, like <em>k</em>-scalar curvature and <em>k</em>-Ricci curvature. In this work, we consider other basic curvature invariants, namely the scalar curvature and <em>δ</em>-Casorati curvatures, and derive new inequalities for such hypersurfaces of a GRW spacetime. We also find the conditions for which the equality cases in these inequalities hold and give some applications in Lorentzian geometry.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"94 ","pages":"Article 102140"},"PeriodicalIF":0.5,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140620987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}