Кафедра математики та фізики

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Перегляд Кафедра математики та фізики по Тема "almost geodesic mapping"
  • Матеріал
    Almost geodesic mappings of affinely connected spaces that preserve the Riemannian curvature
    (Líceum University Press, 2015) Березовський, Володимир Євгенійович ; Berezovskii, V. E.
    In the present paper the authors give some conditions preserved Riemannian curvature tensor with respect to almost geodesic mappings of affinely connected spaces. It is noteworthy that these conditions are valid for other types of mappings. For the almost geodesic mappings of first type, when the Riemannian curvature tensor is invariant, the authors deduce a differential equations system of Cauchy type. In addition the authors investigate almost geodesic mappings of first type, where the Weyl tensor of projective curvature is invariant and Riemannian tensor is not invariant.
  • Матеріал
    Almost geodesic mappings of the fist type onto symmetric spaces
    (Slovak University of Technology in Bratislava, 2017) Березовський, Володимир Євгенійович
    The artscle is devoted to the theory of almost geodesic mappings of the first type onto symmetric spaces. There are found certain necessary and sufficient conditions when a space with affine connection admits a canonical almost geodesic mappings of the first type onto symmetric spaces.
  • Матеріал
    Almost geodesic mappings of the second type of spaces with affine connection onto two-symmetric spaces
    (Spektrum STU, 2019) Березовський, Володимир Євгенійович ; Лещенко, Світлана Валентинівна ; Ненька, Руслана Володимирівна
    In the paper we consider canonical almost geodesic mappings of type _2(e) of spaces with affine connection onto two-symmetric spaces. The main equations for the mappings are obtained as a closed mixed system of PDEs of Cauchy type. We have found the maximum number of essential parameters which the solution of the system depends on.
  • Матеріал
    ALMOST GEODESIC MAPPINGS OF TYPE pi1 OF SPACES WITH AFFINE CONNECTION
    (Society of mathematicians and physicists of Montenegro and Department of Mathematics of The University of Montenegro, 2021) Березовський, Володимир Євгенійович
    We consider almost geodesic mappings of spaces with affine connections. This mappings are a special case of firsttype almost geodesic mappings. We have found the objects which are invariants of the mappings pi1. The fundamental equations of these mappings are in Cauchy form. We study mappings of constant curvature spaces.
  • Матеріал
    Almost geodesic mappings onto generalized Ricci-symmetric manifolds
    (College of Nyíregyháza, 2010) Березовський, Володимир Євгенійович ; Berezovskii, V. E.
    Our aim is to continue investigations concerning existence of almost geodesic mappings of manifolds with linear connection. We deduce necessary and sufficient conditions for existence of the so-called canonical almost geodesic mappings of type π of a manifold endowed with a linear connection onto generalized Ricci-symmetric manifolds. Our result is a generalization of some previous results by N. S. Sinyukov.
  • Матеріал
    Canonical almost geodesic mappings of type π1 onto pseudo-Riemannian manifolds
    (Hackensack, NJ: World Scientific, 2008) Березовський, Володимир Євгенійович ; Berezovskii, V. E.
    In this paper, the authors study properties of canonical almost geodesic mappings of type π˜1 onto pseudo-Riemannian manifolds. They find necessary and sufficient conditions for existence of the canonical almost geodesic mappings of type π˜1 of a manifold endowed with a linear connection onto pseudo-Riemannian manifolds. The conditions are described by means of a closed system of partial differential equations of first order of Cauchy type.
  • Матеріал
    Fundamental PDE’s of the canonical almost geodesic mappings of type π ˜ 1
    (Bull. Malays. Math. Sci. Soc., 2014) Березовський, Володимир Євгенійович ; Berezovskii, V. E.
    For modelling of various physical processes, geodesic lines and almost geodesic curves serve as a useful tool. Trasformations or mappings between spaces (endowed with a metric or a connection) which preserve such curves play an important role in physics, particularly in mechanics, and in geometry as well. In the present article the authors continue investigations concerning existence of almost geodesic mappings of manifolds with linear (affine) connection, particularly of the so-called π ˜ 1 mappings, i.e. canonical almost geodesic mappings of type π ˜ 1 according to Sinyukov. First they give necessary and sufficient conditions for existence of π ˜ 1 mappings of a manifold endowed with a linear connection onto pseudo-Riemannian manifolds. The conditions take the form of a closed system of PDEs of first order of Cauchy type. Further they deduce necessary and sufficient conditions for existence of π ˜ 1 mappings onto generalized Ricci-symmetric spaces. The results are generalizations of some previous theorems obtained by N. S. Sinyukov.
  • Матеріал
    Geodesic and almost geodesic mappings onto Ricci symmetric spaces
    (University of Defence, Brno, Czech Republic, 2017) Березовський, Володимир Євгенійович
    This paper is devoted to study of geodesic and almost geodesic mappings of special spaces with affine connection. In the first section, we mention the basic definition of geodesic and almost geodesic mappings. The next section is devoted to geodesic mappings onto Ricci symmetric manifolds and its fundamental diferential equation in Cauchy type form in covariant derivatives. We also study almost geodesic mappings of the first type onto symmetric space.
  • 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.
  • Матеріал
    On almost geodesic mappings of the type π1 of Riemannian spaces preserving a system n-orthogonal hypersurfaces
    (Palermo: Circolo Matematico di Palermo, 1999) Березовський, Володимир Євгенійович ; Berezovskii, V. E.
    The authors study almost geodesic mappings of the type π1 :Vn →Vn , which preserve systems of n-orthogonal hypersurfaces, and they find Riemannian metrics for which these mappings exist.
  • Матеріал
    On Preservation of the Riemann Tensor With Respect to Some Mappings of Affinely Connected Space
    (Springer Nature, 2018) Березовський, Володимир Євгенійович ; Ковальов, Леонід Євгенійович
    This paper is devoted to geodesic and almost geodesic mappings of affinely connected spaces. We find conditions which ensure that the Riemann tensor is an invariant geometric object with respect to the studied mappings. In this work we present an example of a non-trivial geodesic mapping between the flat spaces.
  • Матеріал
    On special first-type almost geodesic mappings of affine connection spaces preserving a certain tensor
    (Pleiades Publishing, 2015) Березовський, Володимир Євгенійович ; Berezovskii, V. E.
    В настоящей работе изучаются частные случаи канонических почти геодезических отображений первого типа пространств аффинной связности. Основные уравнения рассматриваемых отображений сведены к замкнутой системе типа Коши в ковариантных производных. Установлено количество существенных параметров, от которых зависит общее решение. Приведен пример таких отображений.
  • Матеріал
    О частном случае почти геодезических отображений первого типа пространств аффинной связности, при котором сохраняется некоторый тензор
    (Russian Academy of Sciences, Academizdatcenter "Nauka", 2015) Березовський, Володимир Євгенійович ; Berezovskii, V. E.
    В настоящей работе изучаются частные случаи канонических почти геодезических отображений первого типа пространств аффинной связности. Основные уравнения рассматриваемых отображений сведены к замкнутой системе типа Коши в ковариантных производных. Установлено количество существенных параметров, от которых зависит общее решение. Приведен пример таких отображений.