Differential Geometry of Manifolds of Figures最新文献_第2页

Maps generating normals on a manifold 在流形上生成法线的映射

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2019-50-13

K. Polyakova

{"title":"Maps generating normals on a manifold","authors":"K. Polyakova","doi":"10.5922/0321-4796-2019-50-13","DOIUrl":"https://doi.org/10.5922/0321-4796-2019-50-13","url":null,"abstract":"The first- and second-order canonical forms are considered on a smooth m-manifold. The approach connected with coordinate expressions of basic and fiber forms, and first- and second-order tangent vectors on a manifold is implemented. It is shown that the basic first- and secondorder tangent vectors are first- and second-order Pfaffian (generalized) differentiation operators of functions set on a manifold. Normals on a manifold are considered. Differentials of the basic first-order (second-order) tangent vectors are linear maps from the first-order tangent space to the second-order (third-order) tangent space. Differentials of the basic first-order tangent vectors (basic vectors of the first-order normal) set a map which takes a first-order tangent vector into the second-order normal for the first-order tangent space of (into the third-order normal for second-order tangent space). The map given by differentials of the basic first-order tangent vectors takes all tangent vectors to the vectors of the second-order normal. Such splitting the osculating space in the direct sum of the first-order tangent space and second-order normal defines the simplest (canonical) affine connection which horizontal subspace is the indicated normal. This connection is flat and symmetric. The second-order normal is the horizontal subspace for this connection. Derivatives of some basic vectors in the direction of other basic vectors are equal to values of differentials of the first vectors on the second vectors, and the order of differentials is equal to the order of vectors along which differentiation is made. The maps set by differentials of basic vectors of r-order normal for (r – 1)-order tangent space take the basic first-order tangent vectors to the basic vectors of (r + 1)-order normal for r-order tangent space. Horizontal vectors for the simplest second-order connection are constructed. Second-order curvature and torsion tensors vanish in this connection. For horizontal vectors of the simplest second-order connection there is the decomposition by means of the basic vectors of the secondand third-order normals.","PeriodicalId":114406,"journal":{"name":"Differential Geometry of Manifolds of Figures","volume":"52 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":"133458023","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 conformal transformations of metrics of Riemannian paracomplex manifolds 黎曼拟复流形度量的保角变换

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2020-52-11

S. Stepanov, I. Tsyganok, V. Rovenski

引用次数: 0

The composition equipment for congruence of hypercentredplanes 超中心平面同余的合成设备

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2019-50-8

A. Vyalova

{"title":"The composition equipment for congruence of hypercentred\u0000planes","authors":"A. Vyalova","doi":"10.5922/0321-4796-2019-50-8","DOIUrl":"https://doi.org/10.5922/0321-4796-2019-50-8","url":null,"abstract":"In n-dimensional projective space Pn a manifold Vnm , i. e., a congruence of hypercentered planes Pm , is considered. By a hypercentered planе Pm we mean m-dimensional plane with a (m – 1)-dimensional hyperplane Lm1 , distinguished in it. The first-order fundamental object  of the congruence is a pseudotensor. The principal fiber bundle Gr (Vnm) is associated with the congruence, r  n(n m1)  m2. . The base of the bundle is the manifold Vnm and a typical fiber is the stationarity subgroup Gr of a centered plane Pm . In principal fiber bundle a fundamental-group connection is given using the field of the object Г . The composition equipment for the congruence is set by means of a point lying in the plane and not belonging to its hypercenter and an (n – m – 1)-dimensional plane, which does not have common points with the hypercentered plane. The composition equipment is given by field of quasitensor  . It is proved that the composition equipment for the congruence Vnm of hypercentred m-planes Pm induces a fundamental-group connection with object Г in the principal bundle Gr (Vnm ) associated with the congruence. In proof, the envelopments Г  Г(, ) are built for the components of the connection object Г .","PeriodicalId":114406,"journal":{"name":"Differential Geometry of Manifolds of Figures","volume":"31 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":"115430502","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

Complete Riemannian manifolds with Killing — Ricci and Codazzi — Ricci tensors 具有Killing - Ricci张量和Codazzi - Ricci张量的完备黎曼流形

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2022-53-10

S. Stepanov, I. Tsyganok, J. Mikeš

引用次数: 0

On nonexistence of Kenmotsu structure on аст-hypersurfacesof cosymplectic type of a Kählerian manifold 关于Kählerian流形аст-hypersurfacesof余辛型上Kenmotsu结构的不存在性

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2019-50-3

G. Banaru

{"title":"On nonexistence of Kenmotsu structure on аст-hypersurfaces\u0000of cosymplectic type of a Kählerian manifold","authors":"G. Banaru","doi":"10.5922/0321-4796-2019-50-3","DOIUrl":"https://doi.org/10.5922/0321-4796-2019-50-3","url":null,"abstract":"Almost contact metric (аст-)structures induced on oriented hypersurfaces of a Kählerian manifold are considered in the case when these аст- structures are of cosymplectic type, i. e. the contact form of these structures is closed. As it is known, the Kenmotsu structure is the most important non-trivial example of an almost contact metric structure of cosymplectic type. The Cartan structural equations of the almost contact metric structure of cosymplectic type on a hypersurface of a Kählerian manifold are obtained. It is proved that an almost contact metric structure of cosymplectic type on a hypersurface of a Kählerian manifold of dimension at least six cannot be a Kenmotsu structure. Moreover, it follows that oriented hypersurfaces of a Kählerian manifold of dimension at least six do not admit non-trivial almost contact metric structures of cosymplectic type that belong to any well studied class of аст-structures. The present results generalize some results on almost contact metric structures on hypersurfaces of an almost Hermitian manifold obtained earlier by V. F. Kirichenko, L. V. Stepanova, A. Abu-Saleem, M. B. Banaru and others.","PeriodicalId":114406,"journal":{"name":"Differential Geometry of Manifolds of Figures","volume":"27 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":"127298517","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

Metrics of a space with linear connection which is not semi-symmetric 非半对称的线性连接空间的度量

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2020-53-14

Y. Shevchenko, A. Vyalova

引用次数: 1

Prolonged almost quazi-Sasakian structures 延长了几乎是准sasaki式的结构

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2020-52-7

S. Galaev

引用次数: 0

Vanishing theorems for higher-order Killing and Codazzi 高阶Killing和Codazzi的消失定理

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2019-50-16

S. Stepanov, I. Tsyganok

引用次数: 0

The Grassmann-like manifold of centered planes when a surface is described by the centre 当一个表面由中心来描述时，中心平面的格拉斯曼流形

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2021-52-4

O. Belova

引用次数: 0

On the structure forms of a projective structure 论射影结构的结构形式

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2022-53-7

A. Kuleshov

引用次数: 0