Pub Date : 2023-11-04DOI: 10.1142/s0129167x23500982
Young Jin Suh
The study of Ricci–Bourguignon soliton on real hypersurfaces in the complex two-plane Grassmannian [Formula: see text] is first investigated. It is proved that there exists a shrinking Ricci–Bourguignon soliton on a Hopf real hypersurface [Formula: see text] in [Formula: see text] by using pseudo-anticommuting Ricci tensor. Moreover, we have proved that there does not exist a nontrivial gradient Ricci–Bourguignon soliton [Formula: see text] on real hypersurfaces with isometric Reeb flow in the complex two-plane Grassmannian [Formula: see text]. Among the class of contact hypersurface in [Formula: see text], we also prove that there does not exist a nontrivial gradient Ricci–Bourguignon soliton in [Formula: see text] over the totally geodesic and totally real quaternionic projective space [Formula: see text] in [Formula: see text], [Formula: see text].
{"title":"Real Hypersurfaces with Ricci-Bourguignon Soliton in the Complex Two-Plane Grassmannians","authors":"Young Jin Suh","doi":"10.1142/s0129167x23500982","DOIUrl":"https://doi.org/10.1142/s0129167x23500982","url":null,"abstract":"The study of Ricci–Bourguignon soliton on real hypersurfaces in the complex two-plane Grassmannian [Formula: see text] is first investigated. It is proved that there exists a shrinking Ricci–Bourguignon soliton on a Hopf real hypersurface [Formula: see text] in [Formula: see text] by using pseudo-anticommuting Ricci tensor. Moreover, we have proved that there does not exist a nontrivial gradient Ricci–Bourguignon soliton [Formula: see text] on real hypersurfaces with isometric Reeb flow in the complex two-plane Grassmannian [Formula: see text]. Among the class of contact hypersurface in [Formula: see text], we also prove that there does not exist a nontrivial gradient Ricci–Bourguignon soliton in [Formula: see text] over the totally geodesic and totally real quaternionic projective space [Formula: see text] in [Formula: see text], [Formula: see text].","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135728309","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 : 2023-11-04DOI: 10.1142/s0129167x23501082
Andrea Loi, Fabio Zuddas
Let $P_{lambdaSigma_n}$ be the Ehrhart polynomial associated to an intergal multiple $lambda$ of the standard symplex $Sigma_n subset mathbb{R}^n$. In this paper we prove that if $(M, L)$ is an $n$-dimensional polarized toric manifold with associated Delzant polytope $Delta$ and Ehrhart polynomial $P_Delta$ such that $P_{Delta}=P_{lambdaSigma_n}$, for some $lambda in mathbb{Z}^+$, then $(M, L)cong (mathbb{C} P^n, O(lambda))$ (where $O(1)$ is the hyperplane bundle on $mathbb{C} P^n$) in the following three cases: 1. arbitrary $n$ and $lambda=1$, 2. $n=2$ and $lambda =3$, 3. $lambda =n+1$ under the assumption that the polarization $L$ is asymptotically Chow semistable.
{"title":"Some Characterizations of the Complex Projective Space via Ehrhart Polynomials","authors":"Andrea Loi, Fabio Zuddas","doi":"10.1142/s0129167x23501082","DOIUrl":"https://doi.org/10.1142/s0129167x23501082","url":null,"abstract":"Let $P_{lambdaSigma_n}$ be the Ehrhart polynomial associated to an intergal multiple $lambda$ of the standard symplex $Sigma_n subset mathbb{R}^n$. In this paper we prove that if $(M, L)$ is an $n$-dimensional polarized toric manifold with associated Delzant polytope $Delta$ and Ehrhart polynomial $P_Delta$ such that $P_{Delta}=P_{lambdaSigma_n}$, for some $lambda in mathbb{Z}^+$, then $(M, L)cong (mathbb{C} P^n, O(lambda))$ (where $O(1)$ is the hyperplane bundle on $mathbb{C} P^n$) in the following three cases: 1. arbitrary $n$ and $lambda=1$, 2. $n=2$ and $lambda =3$, 3. $lambda =n+1$ under the assumption that the polarization $L$ is asymptotically Chow semistable.","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775380","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 : 2023-11-03DOI: 10.1142/s0129167x23501045
Debabrata De, Kunal Mukherjee
{"title":"On bounded coordinates in bimodules","authors":"Debabrata De, Kunal Mukherjee","doi":"10.1142/s0129167x23501045","DOIUrl":"https://doi.org/10.1142/s0129167x23501045","url":null,"abstract":"","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135868786","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 : 2023-11-03DOI: 10.1142/s0129167x23501070
Zezhen Sun
In this paper we introduce two $1/kappa^{n}$-type ($nge1$) curvature flows for closed convex planar curves. Along the flows the length of the curve is decreasing while the enclosed area is increasing. And finally, the evolving curves converge smoothly to a finite circle if they do not develop singularity during the evolution process.
{"title":"Two nonlocal inverse curvature flows of convex closed plane curves","authors":"Zezhen Sun","doi":"10.1142/s0129167x23501070","DOIUrl":"https://doi.org/10.1142/s0129167x23501070","url":null,"abstract":"In this paper we introduce two $1/kappa^{n}$-type ($nge1$) curvature flows for closed convex planar curves. Along the flows the length of the curve is decreasing while the enclosed area is increasing. And finally, the evolving curves converge smoothly to a finite circle if they do not develop singularity during the evolution process.","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135868809","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 : 2023-11-03DOI: 10.1142/s0129167x23501069
M. Ferreiro-Subrido, E. Garcia-Rio, R. Vazquez-Lorenzo
{"title":"Geometry of four-dimensional kahler and para-kahler lie groups","authors":"M. Ferreiro-Subrido, E. Garcia-Rio, R. Vazquez-Lorenzo","doi":"10.1142/s0129167x23501069","DOIUrl":"https://doi.org/10.1142/s0129167x23501069","url":null,"abstract":"","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135868784","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 : 2023-11-03DOI: 10.1142/s0129167x23501033
Chuyu Zhou
We compute K-semistable domains for various examples of log pairs.
{"title":"On K-semistable domains - more examples","authors":"Chuyu Zhou","doi":"10.1142/s0129167x23501033","DOIUrl":"https://doi.org/10.1142/s0129167x23501033","url":null,"abstract":"We compute K-semistable domains for various examples of log pairs.","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135868975","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 : 2023-11-03DOI: 10.1142/s0129167x23501057
Yunlong Yang, Lina Liu
{"title":"An anisotropic area-preserving flow and its geometric application","authors":"Yunlong Yang, Lina Liu","doi":"10.1142/s0129167x23501057","DOIUrl":"https://doi.org/10.1142/s0129167x23501057","url":null,"abstract":"","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135868788","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 : 2023-10-28DOI: 10.1142/s0129167x23500970
Rupam Karmakar, Praveen Kumar Roy
Let [Formula: see text] denote the blow-up of [Formula: see text] along [Formula: see text] general lines and [Formula: see text] general points. In this paper, we focus on [Formula: see text]-very ample line bundles on [Formula: see text] and investigate their Seshadri constants with some restrictions on [Formula: see text]. Additionally, we compute the nef cone of [Formula: see text] for [Formula: see text] and study the Seshadri constants of some ample line bundles on it. We also examine the Seshadri constants of some ample line bundles on [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text].
{"title":"Seshadri constants on some blow UPS of Projective Spaces","authors":"Rupam Karmakar, Praveen Kumar Roy","doi":"10.1142/s0129167x23500970","DOIUrl":"https://doi.org/10.1142/s0129167x23500970","url":null,"abstract":"Let [Formula: see text] denote the blow-up of [Formula: see text] along [Formula: see text] general lines and [Formula: see text] general points. In this paper, we focus on [Formula: see text]-very ample line bundles on [Formula: see text] and investigate their Seshadri constants with some restrictions on [Formula: see text]. Additionally, we compute the nef cone of [Formula: see text] for [Formula: see text] and study the Seshadri constants of some ample line bundles on it. We also examine the Seshadri constants of some ample line bundles on [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text].","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136157612","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 : 2023-10-27DOI: 10.1142/s0129167x2350101x
Soham Chakraborty
{"title":"Classification of regular subalgebras of injective type iii factors","authors":"Soham Chakraborty","doi":"10.1142/s0129167x2350101x","DOIUrl":"https://doi.org/10.1142/s0129167x2350101x","url":null,"abstract":"","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136312446","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 : 2023-10-27DOI: 10.1142/s0129167x23501021
Laura Geatti, Andrea Iannuzzi
Let $,G/K,$ be a non-compact irreducible Hermitian symmetric space of rank $,r,$ and let $,NAK,$ be an Iwasawa decomposition of $,G$. By the polydisc theorem, $,AK/K,$ can be regarded as the base of an $,r$-dimensional tube domain holomorphically embedded in $,G/K$. As every $,N$-orbit in $,G/K,$ intersects $,AK/K$ in a single point, there is a one-to-one correspondence between $,N$-invariant domains in $,G/K,$ and tube domains in the product of $,r,$ copies of the upper half-plane in $,C$. In this setting we prove a generalization of Bochner's tube theorem. Namely, an $,N$-invariant domain $,D,$ in $,G/K,$ is Stein if and only if the base $,Omega,$ of the associated tube domain is convex and ``cone invariant". We also obtain a precise description of the envelope of holomorphy of an arbitrary holomorphically separable $,N$-invariant domain over $,G/K$.
{"title":"Geometry of Hermitian symmetric spaces under the action of a maximal unipotent group","authors":"Laura Geatti, Andrea Iannuzzi","doi":"10.1142/s0129167x23501021","DOIUrl":"https://doi.org/10.1142/s0129167x23501021","url":null,"abstract":"Let $,G/K,$ be a non-compact irreducible Hermitian symmetric space of rank $,r,$ and let $,NAK,$ be an Iwasawa decomposition of $,G$. By the polydisc theorem, $,AK/K,$ can be regarded as the base of an $,r$-dimensional tube domain holomorphically embedded in $,G/K$. As every $,N$-orbit in $,G/K,$ intersects $,AK/K$ in a single point, there is a one-to-one correspondence between $,N$-invariant domains in $,G/K,$ and tube domains in the product of $,r,$ copies of the upper half-plane in $,C$. In this setting we prove a generalization of Bochner's tube theorem. Namely, an $,N$-invariant domain $,D,$ in $,G/K,$ is Stein if and only if the base $,Omega,$ of the associated tube domain is convex and ``cone invariant\". We also obtain a precise description of the envelope of holomorphy of an arbitrary holomorphically separable $,N$-invariant domain over $,G/K$.","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136312482","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}
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