Differencialʹnaâ geometriâ mnogoobrazij figur最新文献

A note on n-quasi-umbilical hypersurfaces in almost Hermitian manifolds 几乎厄米流形中n-拟脐超曲面的注释

Differencialʹnaâ geometriâ mnogoobrazij figur Pub Date : 2023-01-01 DOI: 10.5922/0321-4796-2023-54-1-3

M. B. Banaru

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The head of the Kaliningrad geometric school Vladislav Stepanovich Malakhovsky 加里宁格勒地理学校的校长弗拉季斯拉夫·斯捷潘诺维奇·马拉霍夫斯基说

Differencialʹnaâ geometriâ mnogoobrazij figur Pub Date : 2023-01-01 DOI: 10.5922/0321-4796-2023-54-1-1

M. V. Kretov, Yu. I. Shevchenko

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On connections with torsion on nonholonomic para-Kenmotsu manifolds 非完整拟肯-莫苏流形上带扭转的连接

Differencialʹnaâ geometriâ mnogoobrazij figur Pub Date : 2023-01-01 DOI: 10.5922/0321-4796-2023-54-1-6

A. V. Bukusheva

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On the geometry of sub-Riemannian manifolds equipped with a canonical quarter-symmetric connection 具有正则四分之一对称连接的亚黎曼流形的几何性质

Differencialʹnaâ geometriâ mnogoobrazij figur Pub Date : 2023-01-01 DOI: 10.5922/0321-4796-2023-54-1-7

S. V. Galaev

{"title":"On the geometry of sub-Riemannian manifolds equipped with a canonical quarter-symmetric connection","authors":"S. V. Galaev","doi":"10.5922/0321-4796-2023-54-1-7","DOIUrl":"https://doi.org/10.5922/0321-4796-2023-54-1-7","url":null,"abstract":"In this article, a sub-Riemannian manifold of contact type is understood as a Riemannian manifold equipped with a regular distribution of codimension-one and by a unit structure vector field orthogonal to this distribution. This vector field is called a structural. On a sub-Riemannian manifold of contact type, a quarter-symmetric connection is defined, which is associated with an endomorphism that preserves the distribution of the sub-Riemannian manifold. It is proved that if the connection under study is metric, then the endomorphism associated to it is uniquely defined. The structure of the associated endomorphism is found. In the case when the structure vector field is a field of infinitesimal isometries, the quarter-symmetric connection is called the canonical N-connection. An expression is found for the curvature tensor of the canonical N-connection in terms of the Riemann curvature tensor. The properties of the Schouten curvature tensor are investigated, which provide, in particular, the necessary symmetries of the curvature tensor of an N-connection for its sectional curvature to be well-defined. A relation between the sectional curvature of the canonical N-connection and the sectional curvature of the Levi-Civita connection is found. Necessary and sufficient conditions are found under which the sectional curvature of the N-connection and the sectional curvature of the Levi-Civita connection coincide.","PeriodicalId":479751,"journal":{"name":"Differencialʹnaâ geometriâ mnogoobrazij figur","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135103881","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 the type constancy of some six-dimensional planar submanifolds of Cayley algebra Cayley代数中某些六维平面子流形的类型常数

Differencialʹnaâ geometriâ mnogoobrazij figur Pub Date : 2023-01-01 DOI: 10.5922/0321-4796-2023-54-1-2

G. A. Banaru

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On the most important achievements of V. F. Kirichenko in Theory of differentiable manifolds 论V. F. Kirichenko在可微流形理论中的最重要成就

Differencialʹnaâ geometriâ mnogoobrazij figur Pub Date : 2023-01-01 DOI: 10.5922/0321-4796-2023-54-1-4

M. B. Banaru, G. A. Banaru

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Hyperband distribution equipped with a field of conjugate planes 具有共轭平面场的超带分布

Differencialʹnaâ geometriâ mnogoobrazij figur Pub Date : 2023-01-01 DOI: 10.5922/0321-4796-2023-54-1-8

N. A. Eliseeva, Yu. I. Popov

{"title":"Hyperband distribution equipped with a field of conjugate planes","authors":"N. A. Eliseeva, Yu. I. Popov","doi":"10.5922/0321-4796-2023-54-1-8","DOIUrl":"https://doi.org/10.5922/0321-4796-2023-54-1-8","url":null,"abstract":"In this paper, we study a special class of hyperbands, i. e., a framed hyperband distribution. The study of hyperbands and their generalizations in spaces with different fundamental groups is of great interest in connection with numerous applications in mathematics and physics. A special place is occupied by regular hyperstrips, for which the characteristic planes of families of principal tangent hyperplanes do not contain directions tangent to the basal surface of the hyperstrip. In this paper, we use the method of external differential forms of E. Cartan and the group-theoretic method of G. F. Laptev. We consider a regular hyperband distribution of an affine space equipped with a field of conjugate planes with respect to an asymptotic bundle of tensors of the basic surface. The definition of the studied hyperband distribution in the affine space with respect to the 1st order frame is given and the existence theorem is proved. A sequence of fundamental geometric objects of the 1st and 2nd order of a hyperband distribution equipped with a field of conjugate planes is constructed. Fields of quasitensors are constructed that define the fields of normals of the first kind of the distribution of the characteristics of the hyperband distribution. In a differential neighborhood of the 2nd order, the fields of Transon normals of the 1st and 2nd kind are constructed. The conditions for the coincidence of the Transon normal and the Blaschke normal are found.","PeriodicalId":479751,"journal":{"name":"Differencialʹnaâ geometriâ mnogoobrazij figur","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135103866","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}

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The deformation pseudotensor of connections in cocongruence K (n - m)m 共余K (n - m)m中连接的变形伪张量

Differencialʹnaâ geometriâ mnogoobrazij figur Pub Date : 2023-01-01 DOI: 10.5922/0321-4796-2023-54-1-5

O. O. Belova

{"title":"The deformation pseudotensor of connections in cocongruence K (n - m)m","authors":"O. O. Belova","doi":"10.5922/0321-4796-2023-54-1-5","DOIUrl":"https://doi.org/10.5922/0321-4796-2023-54-1-5","url":null,"abstract":"The Grassmann manifold is the set of all -dimensional planes of an -dimensional projective space, with dim. One of the submanifolds of the Grassmann manifold is a complex of -planes if the dimension of the complex exceeds the difference . We continue to study the cocongruence of -dimensional planes using the Cartan — Laptev method. In an -dimensional projective space, the cocongruence of -dimensional planes can be given by the following equations . Compositional equipment of a given cocongruence by fields of ()-planes : and points allows one to define connections of three types in the associated bundle, and one of the three connections is average with respect to the other two. The deformation of these connections is considered and it is shown that the object of deformation is a pseudotensor. We introduce the deformation object of the connection of the second type with respect to the connection of the first type. The deformation of the connection of the third type with respect to the connection of the first type is , and the deformation of the connection of the third type with respect to the connection of the second type is . In the present paper, we use the method of continuations and coverages of G. F. Laptev with assignment of connections in the principal bundle.","PeriodicalId":479751,"journal":{"name":"Differencialʹnaâ geometriâ mnogoobrazij figur","volume":"156 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135103888","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