Differential Geometry of Manifolds of Figures最新文献_第3页

Fields of geometric objects associated with compiled hyperplane H ( ,L)  -distribution in affine space 与编译超平面H (，L)相关的几何对象的场-仿射空间中的分布

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2020-52-10

Yu. I. Popov

{"title":"Fields of geometric objects associated with compiled hyperplane H ( ,L)  -distribution in affine space","authors":"Yu. I. Popov","doi":"10.5922/0321-4796-2020-52-10","DOIUrl":"https://doi.org/10.5922/0321-4796-2020-52-10","url":null,"abstract":"In the first-order frame a tangentially r-framed hyperband is given in the projective space. For simplicity of presentation, we adapt the frame by the field of the 1st kind normals. The tensor of nonholonomicity of clothing L-planes field is introduced. The vanishing the nonholonomic tensor leads to three different interpretations of the hyperband. With the help of ТL-virtual normals of the 1st and 2nd kind of framed L-planes, we come to the following conclusion: in a third order differential neighborhood the bundle of the hyperband second kind normals generates a one-parameter bundle of ТL-virtual first and second kind normals, which correspond to each other in bijection. We consider focal images associated with the hyperband, with the help of which the Norden — Timofeev plane of the indicated hyperband is constructed. The geometric interpretation of the object defining the Norden — Timofeev surface was found by R. F. Dombrovsky for tangentially r-framed surfaces in the projective space. We note that the field of ТL-virtual first kind normals induces the field of the Norden — Timofeev planes, this is the field of the 2nd kind regular hyperband normals. It is proved that with each the 1st kind ТL-virtual normal is induced a bundle of Cartan planes in the 1st kind normal at a fixed point of the hyperband.\u0000In conclusion, we consider the p-structures of the tangent planes field at the base surface of the hyperband.","PeriodicalId":114406,"journal":{"name":"Differential Geometry of Manifolds of Figures","volume":"19 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":"121656139","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

Curvature tensor of connection in principal bundleof Cartan's projective connection space Cartan射影连接空间主束中连接的曲率张量

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/10.5922/0321-4796-2019-50-5

K. Bashashina

引用次数: 0

On stability of Hermitian structures on 6-dimensional planar submanifolds of Cayley algebra Cayley代数6维平面子流形上厄米结构的稳定性

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2021-52-3

M. Banaru, G. Banaru

引用次数: 2

About an analogue of Neifeld’s connectionon the space of centred planes with one-index basic-fibre forms 关于奈菲尔德连接的一种类似的单折射率基本纤维形式的中心平面空间

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2019-50-6

Е. Belova, O. Belova

引用次数: 0

Generalized bilinear connection on the space of centered planes 中心平面空间上的广义双线性连接

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2022-53-3

O. Belova

引用次数: 0

On geometry of Kenmotsu manifolds with N-connection 关于n -连接的Kenmotsu流形的几何

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2019-50-7

A. Bukusheva

{"title":"On geometry of Kenmotsu manifolds with N-connection","authors":"A. Bukusheva","doi":"10.5922/0321-4796-2019-50-7","DOIUrl":"https://doi.org/10.5922/0321-4796-2019-50-7","url":null,"abstract":"A Kenmotsu manifold with a given N-connection is considered. From the integrability of the distribution of a Kenmotsu manifold it follows that the N-connection belongs to the class of the quarter-symmetric connections. Among the N-connections, the class of connections adapted to the structure of the Kenmotsu manifold is specified. In particular, it is proved that an N-connection preserves the structure endomorphism φ of the Kenmotsu manifold if and only if the endomorphisms N and φ commute. A formula expressing the N-connection in terms of the Levi-Civita connection is obtained. The Chrystoffel symbols of the Levi-Civita connection and of the N-connection of the Kenmotsu manifold with respect to the adapted coordinates are computed. The properties of the invariants of the interior geometry of the Kenmotsu manifolds are investigated. The invariants of the interior geometry are the following: the Schouten curvature tensor; the 1-form  defining the distribution D; the Lie derivative 0   L g of the metric tensor g along the vector field ;  the tensor field P with the components given with respect to the adapted coordinate system by the formula Pacd  ncad . The field P is called in the work the Schouten — Wagner tensor. It is proved that the Schouten — Wagner tensor of the interior connection of the Kenmotsu manifold is zero. The conditions that satisfies the endomorphism N defining the metric N-connection are found. At the end of the work, an example of a Kenmotsu manifold with a metric N-connection preserving the structure endomorphism φ is given.","PeriodicalId":114406,"journal":{"name":"Differential Geometry of Manifolds of Figures","volume":"47 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":"123085261","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: 1

On six-dimensional Vaisman — Gray submanifolds ofthe octave algebra 八度代数的六维Vaisman - Gray子流形

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/10.5922/0321-4796-2019-50-4

M. Banaru

引用次数: 0

The composite equipment for manifold of hypercentered planes, whose dimension coincides with dimension of generating plane 一种尺寸与生成平面尺寸一致的超心平面流形复合设备

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2021-52-6

A. Vyalova, Y. Shevchenko

{"title":"The composite equipment for manifold of hypercentered planes, whose dimension coincides with dimension of generating plane","authors":"A. Vyalova, Y. Shevchenko","doi":"10.5922/0321-4796-2021-52-6","DOIUrl":"https://doi.org/10.5922/0321-4796-2021-52-6","url":null,"abstract":"In n-dimensional projective space Pn a manifold , i. e., a family of pairs of planes one of which is a hyperplane in the other, is considered. A principal bundle arises over it, . A typical fiber is the stationarity subgroup of the generator of pair of planes: external plane and its multidimensional center — hyperplane. The principal bundle contains four factor-bundles.\u0000\u0000A fundamental-group connection is set by the Laptev — Lumiste method in the associated fibering. It is shown that the connection object contains four subobjects that define connections in the corresponding factor-bundles. It is proved that the curvature object of fundamental-group connection forms pseudotensor. It contains four subpseudotensors, which are curvature objects of the corresponding subconnections.\u0000\u0000The composite equipment of the family of hypercentered planes 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. It is proved, that composite equipment induces the fundamental-group connections of two types in the associated fibering.","PeriodicalId":114406,"journal":{"name":"Differential Geometry of Manifolds of Figures","volume":"1 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":"129097938","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

Complexes of ellipsoids with indicatrices of coordinate vectors in the form of surfaces 以曲面形式表示坐标向量的椭球的配合物

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2020-52-8

M. Kretov

{"title":"Complexes of ellipsoids with indicatrices of coordinate vectors in the form of surfaces","authors":"M. Kretov","doi":"10.5922/0321-4796-2020-52-8","DOIUrl":"https://doi.org/10.5922/0321-4796-2020-52-8","url":null,"abstract":"The study continues in a three-dimensional affine space of complexes of three-parameter families of ellipsoids, considered earlier in a number of works by the author. A variety of ellipsoids is studied when the ends of the coordinate vectors coincide with the focal points, and the first coordinate straight line describes a cylindrical surface, while on the generating element there are at least three focal points that do not lie on one straight line and on one plane passing through center, and defining three conjugate directions. A complex of ellipsoids is distinguished from the indicated manifold provided that the indicatrices of the second and third coordinate vectors describe surfaces with tangent planes parallel to the third coordinate plane, and the end of the second coordinate vector describes a line with a tangent parallel to the first coordinate vector. An existence theorem for the variety under study is proved. The geometric properties of the complex under consideration are found. It is proved that the end of the first coordinate vector, points of the first coordinate line, and also the first coordinate plane describe a two-parameter family of planes, the end of the third coordinate vector describes a two-parameter family of cylindrical planes, a point of the third coordinate plane describes a one-parameter family of lines with tangents parallel to the first coordinate vector. The characteristic manifold of a generating element consists of six points: the vertex of the frame, three ends of the coordinate vectors, and two ends: the sum of the first and second coordinate vectors, as well as the sum of the first and third coordinate vectors. The focal manifold of the ellipsoid, the complex under study, consists of only three points, which are the ends of the coordinate vectors.","PeriodicalId":114406,"journal":{"name":"Differential Geometry of Manifolds of Figures","volume":"1 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":"134646548","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

Deformation of one-sided surfaces 单面变形

Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2020-52-14

M. Cheshkova

引用次数: 0