Кафедра математики та фізики

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Перегляд Кафедра математики та фізики по Тема "affine connection"
  • Матеріал
    Conformal mappings of Riemannian manifolds preserving the generalized Einstein tensor
    (Slovak University of Technology in Bratislava, 2018) Березовський, Володимир Євгенійович
    We study conformal mappings preserving the generalized Einstein tensor. We have derived corresponding partial differential equations and their integrability conditions. In addition to the generalized Einstein tensor we got other invariants of the mappings. Also we have proved that orientable compact manifolds equipped by positive definite metric, do not admit conformal mappings preserving the generalized Einstein tensor.
  • Матеріал
    Differential Geometry of Special Mappings
    (Olomouc: Palacký University, 2015) Березовський, Володимир Євгенійович ; Berezovskii, V. E.
    During the last 50 years, many new and interesting results have appeared in the theory of conformal, geodesic, holomorphically projective, F-planar and others mappings and transformations of manifolds with affine connection, Riemannian, K¨ahler and Riemann-Finsler manifolds. The authors dedicate the present monograph to the exposition of this topic. We give the basic concepts of the theory of manifolds with affine connection, Riemannian, K¨ahlerian and Riemann-Finsler manifolds, using the notation from. Unless otherwise stated, the investigations are carried out in tensor form, locally, in the class of sufficiently smooth real functions. The dimension n of the spaces under consideration is supposed to be higher than two, as a rule. This fact is not explicitly stipulated in the text. All the spaces are assumed to be connected. Under Riemannian manifolds we mean both positive as well as pseudo-Riemannian manifolds.
  • Матеріал
    INFINITESIMAL CONFORMAL TRANSFORMATIONS OF RIEMANNIAN MANIFOLDS WHICH PRESERVE THE GENERALIZED EINSTEIN TENSOR
    (Institute of Mathematics and Physics, SjF STU in Bratislava, 2020) Березовський, Володимир Євгенійович ; Ненька, Руслана Володимирівна ; Лещенко, Світлана Валентинівна
    We study conformal transformations leaving the generalized Einstein tensor invariant. We have obtained the system of partial differential equations for the transformations, and explored its integrability conditions. Hence we have got the necessary and sufficient conditions in order that a manifold admit a group of conformal motions, preserving the generalized Einstein tensor. Also we have estimated the number of parameters which the group depends on.
  • Матеріал
    On a classification of almost geodesic mappings of affine connection spaces
    (Palacký University Olomouc, 1996) Березовський, Володимир Євгенійович ; Berezovskii, V. E.
    A classification of almost geodesic mappings is given. It is proved that, if an almost geodesic mapping f is simultaneously π1 and π2 (or π3 ), then f is a mapping of affine connection spaces with preserved linear (or quadratic) complex of geodesic lines.