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Contigious hyperquadrics of coequipped hyperbands sHm 共装备超带sHm的连续超二次曲面
Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2019-50-14
Yu. I. Popov
{"title":"Contigious hyperquadrics of coequipped hyperbands sHm","authors":"Yu. I. Popov","doi":"10.5922/0321-4796-2019-50-14","DOIUrl":"https://doi.org/10.5922/0321-4796-2019-50-14","url":null,"abstract":"We consider hyperquadrics that are internally connected to coequipped hyperbands in the projective space. Specifically, a hyperquadric Qn1 tangent to a hyperplane at the point is called a contiguous hyper quadric of a hyperband if it has a second-order contact with the base surface of the hyperband. In a the third order differential neighborhood of the forming element of the hyperband, two two-parameter bundles of fields of adjoining hyperquadrics are internally invariantly joined, their equations are given in a dot frame. The set of hyperquadrics such that the plane and the plane of Cartan are conjugate with respect to hyperquadric Qn1 is considered. The condition is shown under which the normal of the 2nd kind and the Cartan plane are conjugate with respect to the hyperquadric Qn1 . In addition, the following theorem is proved: normalization of a coequipped regular hyperband has a semi-internal equipment if and only if its normals of the first and second kind are polarly conjugate with respect to the hyperquadric.","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":"123435191","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
Сurvature-torsion tensor for Cartan connection Сurvature-torsion张量用于Cartan连接
Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2019-50-18
Y. Shevchenko
{"title":"Сurvature-torsion tensor for Cartan connection","authors":"Y. Shevchenko","doi":"10.5922/0321-4796-2019-50-18","DOIUrl":"https://doi.org/10.5922/0321-4796-2019-50-18","url":null,"abstract":"A Lie group containing a subgroup is considered. Such a group is a principal bundle, a typical fiber of this principal bundle is the subgroup and a base is a homogeneous space, which is obtained by factoring the group by the subgroup. Starting from this group, we constructed structure equations of a space with Cartan connection, which generalizes the Cartan point projective connection, Akivis’s linear projective connection, and a plane projective connection. Structure equations of this Cartan connection, containing the components of the curvature-torsion object, allowed: 1) to show that the curvature-torsion object forms a tensor containing a torsion tensor; 2) to find an analogue of the Bianchi identities such that the curvature-torsion tensor and its Pfaff derivatives satisfy this analogue; 3) to obtain the conditions for the transformation of Pfaffian derivatives of the curvature-torsion tensor into covariant derivatives with respect to the Cartan connection.","PeriodicalId":114406,"journal":{"name":"Differential Geometry of Manifolds of Figures","volume":"75 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":"114865659","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
Examples of surfaces of constant mean curvature 等平均曲率曲面的例子
Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2019-50-17
M. Cheshkova
{"title":"Examples of surfaces of constant mean curvature","authors":"M. Cheshkova","doi":"10.5922/0321-4796-2019-50-17","DOIUrl":"https://doi.org/10.5922/0321-4796-2019-50-17","url":null,"abstract":"A surface in E3 is called parallel to the surface M if it consists of the ends of constant length segments, laid on the normals to the surfaces M at points of this surface. The tangent planes at the corresponding points will be parallel. For surfaces in E3 the theorem of Bonnet holds: for any surface M that has constant positive Gaussian curvature, there exists a surface parallel to it with a constant mean curvature. Using Bonnet's theorem for a surfaces of revolution of constant positive Gaussian curvature, surfaces of constant mean curvature are constructed. It is proved that they are also surfaces of revolution. A family of plane curvature lines (meridians) is described by means of elliptic integrals. The surfaces of constant Gaussian curvature are also described by means of elliptic integrals. Using the mathematical software package, the surfaces under consideration are constructed.","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":"129718305","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 geometry of generalized nonholonomic Kenmotsu manifolds 广义非完整Kenmotsu流形的几何性质
Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2020-53-4
A. Bukusheva
{"title":"On the geometry of generalized nonholonomic Kenmotsu manifolds","authors":"A. Bukusheva","doi":"10.5922/0321-4796-2020-53-4","DOIUrl":"https://doi.org/10.5922/0321-4796-2020-53-4","url":null,"abstract":"The concept of a generalized nonholonomic Kenmotsu manifold is introduced. In contrast to the previously defined nonholonomic Kenmotsu manifold, the manifold studied in the article is an almost normal almost contact metric manifold of odd rank. The manifold is equipped with a metric connection with torsion, which is called the canonical connection in this work. The main properties of the canonical connection are studied. The canonical connection is an analogue of the generalized Tanaka-Webster connection. In this paper, we prove that the canonical connection is the only metric connection with torsion of a special structure that pre­serves the structural 1-form and the Reeb vector field. We study the in­trinsic geometry of a generalized nonholonomic Kenmotsu manifold equipped with a canonical connection. It is proved that if a generalized nonholonomic Kenmotsu manifold is an Einstein manifold with respect to a canonical connection, then it is Ricci-flat with respect to this connec­tion. An example of a generalized nonholonomic Kenmotsu manifold that is not a nonholonomic Kenmotsu manifold is given.","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":"129976054","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
Professor Oldřich Kowalski passed away Oldřich Kowalski教授去世了
Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2021-52-1
M. Abbassi, J. Mikeš, A. Vanžurová, C. Bejan, O. Belova
{"title":"Professor Oldřich Kowalski passed away","authors":"M. Abbassi, J. Mikeš, A. Vanžurová, C. Bejan, O. Belova","doi":"10.5922/0321-4796-2021-52-1","DOIUrl":"https://doi.org/10.5922/0321-4796-2021-52-1","url":null,"abstract":"This paper is dedicated to the me­mo­ry of Professor Kowalski who was one of the leading re­sear­chers in the field of dif­fe­ren­tial geometry and especially Rie­mannian and affine geometry. He signif­icantly contributed to rai­sing the level of teaching dif­fe­ren­tial geometry by careful and sys­tematic preparation of lectures for students. Prof. Kowalski is the author or co-author of more than 170 professional articles in internation­ally recognized jour­nals, two monographs, text books for students. Prof. Kowalski collaborated with many mathematicians from other countries, particularly from Belgium, Italy, Ja­pan, Romania, Russia, Morocco, Spain and others. With the death of Professor Oldřich Kowalský mathe­matical community are losing a significant personality and an exceptional colleague, a kind and dedicated teacher, a man of high moral qualities.","PeriodicalId":114406,"journal":{"name":"Differential Geometry of Manifolds of Figures","volume":"283 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113972315","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 nearly Kählerian manifolds and quasi-Sasakian hypersurfaces axiom 近似Kählerian流形与拟sasaki超曲面公理
Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2021-52-2
G. Banaru
{"title":"On nearly Kählerian manifolds and quasi-Sasakian hypersurfaces axiom","authors":"G. Banaru","doi":"10.5922/0321-4796-2021-52-2","DOIUrl":"https://doi.org/10.5922/0321-4796-2021-52-2","url":null,"abstract":"It is known that an almost contact metric structure is induced on an arbitrary hypersurface of an almost Hermitian manifold. The case when the almost Hermitian manifold is nearly Kählerian and the almost contact metric structure on its hypersurface is quasi-Sasakian is considered. It is proved that non-Kählerian nearly Kählerian manifolds (in particular, the six-dimensional sphere equipped with the canonical nearly Kählerian structure) do not satisfy to the quasi-Sasakian hypersurfaces axiom.","PeriodicalId":114406,"journal":{"name":"Differential Geometry of Manifolds of Figures","volume":"11 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":"114283512","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
Pencils of circles with a straight line and circle asthe basic elements 以直线和圆为基本元素的圆铅笔
Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2019-50-19
E. Shemyakina
{"title":"Pencils of circles with a straight line and circle as\u0000the basic elements","authors":"E. Shemyakina","doi":"10.5922/0321-4796-2019-50-19","DOIUrl":"https://doi.org/10.5922/0321-4796-2019-50-19","url":null,"abstract":"Pencils of circles with are a straight line and a circle as the basic elements are investigated. Three cases of arrangement of a basic straight line and a circle are considered: when the straight line does not intersect a circle, when the straight line and a circle have one generic point, and when the straight line intersects a circle in two points. A parameter is entered and the equations of new pencils of circles are registered. By means of mathematical manipulations the obtained equations are given to the initial equation of a circle. Different values are attached to the parameter and the circles belonging to new pencils are constructed. Based on the obtained graphs it is concluded that the pencil with not intersecting basic straight line and a circle forms a hyperbolic pencil of circles, a pencil with a basic straight line and a circle having one generic point forms a parabolic pencil, and a pencil with the intersecting basic straight line and a circle forms an elliptic pencil.","PeriodicalId":114406,"journal":{"name":"Differential Geometry of Manifolds of Figures","volume":"147 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":"123486935","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
Induced connections of two types on a surface of an affinespace 仿射空间表面上两种类型的感应连接
Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/10.5922/0321-4796-2019-50-20
A. Shults
{"title":"Induced connections of two types on a surface of an affine\u0000space","authors":"A. Shults","doi":"10.5922/10.5922/0321-4796-2019-50-20","DOIUrl":"https://doi.org/10.5922/10.5922/0321-4796-2019-50-20","url":null,"abstract":"In the affine space the fundamental-group connection in the bundle associated with a surface as a manifold of tangent planes is investigated. The principal bundle contains a quotient bundle of tangent frames, the typical fiber of which is a linear group acting in a centered tangent plane and a quotient bundle of normal frames, the typical fiber of which is a linear group acting inefficiently in a normal quotient space. The curvature object of the fundamental-group connection is a tensor that contains two primary subtensors tangent and normal linear connections. The tensor of non-absolute parallel transference is constructed. Two envelopment of the connection object is obtained. Analytic and geometric conditions of coincidence of two types of envelopment are found. The covariant derivatives of equipping quasitensor form a tensor. The alternations of the covariant derivatives of the objects of the affine and linear connections of the first type are equal to the corresponding components of the curvature tensor and for the second type they vanish.","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":"129792490","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
Finding symmetries for the problem of water waves with surface tension 寻找具有表面张力的水波问题的对称性
Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2022-53-13
E. Shamardina
{"title":"Finding symmetries for the problem of water waves with surface tension","authors":"E. Shamardina","doi":"10.5922/0321-4796-2022-53-13","DOIUrl":"https://doi.org/10.5922/0321-4796-2022-53-13","url":null,"abstract":"T. Brooke Benjamin and P. J. Olver “Hamiltonian structure, symmet­ries and conservation laws for water waves” study the behavior of Hamil­to­nian systems with an infinite-dimensional phase space. The methods of va­riational problems and infinite-dimensional differential geometry are applicable to this problem. A special case of the problem is an abstract prob­lem of hydrodynamics for an ideal fluid. Its configuration space is the group of volume-preserving diffeomorphisms of some manifold in or filled with fluid. Even more special is the problem of waves on water. Its non-standard nature is due to the presence of boundary con­di­tions on the free surface. These boundary conditions can be interpreted in terms of the functional derivatives of the energy integral, which plays the role of the Hamiltonian. Here we consider in detail the case of this prob­lem in R2, taking into account surface tension, and find symmetries for it, which was not considered in detail in the article. Finding symmet­ries can be achieved without recourse to the Hamiltonian structure of the gi­ven problem.","PeriodicalId":114406,"journal":{"name":"Differential Geometry of Manifolds of Figures","volume":"83 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":"125416090","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 elliptic cylinders with a characteristicmanifold of the generator element in the form of coordinatestraight lines 具有发电机元件特征流形的椭圆圆柱体以坐标直线的形式构成
Differential Geometry of Manifolds of Figures Pub Date : 1900-01-01 DOI: 10.5922/0321-4796-2019-50-10
M. Kretov
{"title":"Complexes of elliptic cylinders with a characteristic\u0000manifold of the generator element in the form of coordinate\u0000straight lines","authors":"M. Kretov","doi":"10.5922/0321-4796-2019-50-10","DOIUrl":"https://doi.org/10.5922/0321-4796-2019-50-10","url":null,"abstract":"The complex (three-parameter family) of elliptic cylinders is investigated in the three-dimensional affine space, in which the characteristic multiplicity of the forming element consists of three coordinate axes. The focal variety of the forming element of the considered variety is geometrically characterized. Geometric properties of the complex under study were obtained. It is shown that the studied manifold exists and is determined by a completely integrable system of differential equations. It is proved that the focal variety of the forming element of the complex consists of four geometrically characterized points. The center of the ray of the straight-line congruence of the axes of the cylinder, the indicatrix of the second coordinate vector, the second coordinate line and one of the coordinate planes are fixed. The indicatrix of the first coordinate vector describes a one-parameter family of lines with tangents parallel to the second coordinate vector. The end of the first coordinate vector describes a one-parameter family of lines with tangents parallel to the third coordinate vector. The indicatrix of the third coordinate vector and its end describe congruences of planes parallel to the first coordinate plane. The points of the first coordinate line and the first coordinate plane describe one-parameter families of planes parallel to the coordinate plane indicated above.","PeriodicalId":114406,"journal":{"name":"Differential Geometry of Manifolds of Figures","volume":"35 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":"124502577","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
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