Differential Geometry of Manifolds of Figures最新文献_第5页

A geometric model of linear fractional transformations 线性分数变换的几何模型

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2022-53-8

S. Matsievsky

引用次数: 1

On quasi-Sasakian structure on a totally umbilical hypersurface of a six-dimensional Hermitian planar submanifold of Cayley algebra Cayley代数的六维厄米平面子流形的全脐超曲面上的拟sasakian结构

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2022-53-1

G. Banaru

引用次数: 1

Affine transformations of the tangent bundle with a complete lift connection over a manifold with a linear connection of special type 具有特殊类型线性连接的流形上具有完全提升连接的切束的仿射变换

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2021-52-13

A. Y. Sultanov, G. A. Sultanova, N.V. Sadovnikov

{"title":"Affine transformations of the tangent bundle with a complete lift connection over a manifold with a linear connection of special type","authors":"A. Y. Sultanov, G. A. Sultanova, N.V. Sadovnikov","doi":"10.5922/0321-4796-2021-52-13","DOIUrl":"https://doi.org/10.5922/0321-4796-2021-52-13","url":null,"abstract":"The theory of tangent bundles over a differentiable manifold M belongs to the geometry and topology of manifolds and is an intensively developing area of the theory of fiber spaces. The foundations of the theory of fibered spaces were laid in the works of S. Eresman, A. Weil, A. Morimoto, S. Sasaki, K. Yano, S. Ishihara. Among Russian scientists, tangent bundles were investigated by A. P. Shirokov, V. V. Vishnevsky, V. V. Shurygin, B. N. Shapukov and their students.\u0000\u0000In the study of automorphisms of generalized spaces, the question of infinitesimal transformations of connections in these spaces is of great importance. K. Yano, G. Vrancianu, P. A. Shirokov, I. P. Egorov, A. Z. Petrov, A. V. Aminova and others have studied movements in different spaces. The works of K. Sato and S. Tanno are devoted to the motions and automorphisms of tangent bundles. Infinitesimal affine collineations in tangent bundles with a synectic connection were considered by H. Shadyev.\u0000\u0000At present, the question of the motions of fibered spaces is considered in the works of A. Ya. Sultanov, in which infinitesimal transformations of a bundle of linear frames with a complete lift connection, the Lie algebra of holomorphic affine vector fields in arbitrary Weyl bundles are investigated. In this paper we obtain exact upper bounds for the dimensions of Lie algebras of infinitesimal affine transformations in tangent bundles with a synectic connection A. P. Shyrokov.","PeriodicalId":114406,"journal":{"name":"Differential Geometry of Manifolds of Figures","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124288163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Invariance of some classes of almost Hermitian structures concerning to the one-parameter group of diffeomorphisms generated by the Lie vector field 李向量场生成的单参数群的微分同态的几类概厄密结构的不变性

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2022-53-12

S. V. Khokhlov, L. Ignatochkina

{"title":"Invariance of some classes of almost Hermitian structures concerning to the one-parameter group of diffeomorphisms generated by the Lie vector field","authors":"S. V. Khokhlov, L. Ignatochkina","doi":"10.5922/0321-4796-2022-53-12","DOIUrl":"https://doi.org/10.5922/0321-4796-2022-53-12","url":null,"abstract":"Finding the conditions for the invariance of geometric objects under the action of transformation groups is one of the main objects of geometric research. Almost Hermitian structures and structures of the Gray — Hervella classification on smooth manifolds are considered in this paper. All arguments are given using invariant Koszul’s calculus. Conditions for the invariance of the Kähler form in type structures are investigated and it is shown that the Kähler form is covariantly constant with respect to the Lie vector field. Conditions for the invariance of the Riemannian metric under the action of a one-parameter group of diffeomorphisms generated by a Lie vector field are studied. A criterion for the invariance of an almost complex structure with respect to the local group of diffeomorphisms generated by the Lie vector field in the class W4 is proved. Conditions for the invariance of an operator of an almost complex structure, a tensor of a Riemannian metric, are proved. It is established that the invariance of the Riemannian structure g implies the invariance of the operator of an almost complex structure for some class of manifolds according to the Gray — Hervella classification, and conditions for the covariant constancy of the Lie form in certain classes of manifolds of dimensions above four were obtained. It is proved that the Lie form is covariantly constant in some classes of the type of dimensions above four.","PeriodicalId":114406,"journal":{"name":"Differential Geometry of Manifolds of Figures","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128028219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On some characteristics of subset of prime numbers 关于素数子集的一些特征

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2019-50-12

V. Malakhovsky

引用次数: 0

The founder of of the Kaliningrad Scientific Geometrical School Vladislav Stepanovich Malakhovsky 加里宁格勒科学几何学校的创始人弗拉季斯拉夫·斯捷潘诺维奇·马拉霍夫斯基

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2019-50-1

M. Kretov, T. Funtikova, Y. Shevchenko

引用次数: 1