Кафедра математики та фізики

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Перегляд Кафедра математики та фізики по Автор "Березовський, Володимир Євгенійович"
  • 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 first type on spaces with affine connection onto symmetric spaces
    (Kharkiv Mathematical Society, 2016) Березовський, Володимир Євгенійович ; Berezovsky, V.E.
  • Матеріал
    Almost geodesic mappings of spaces with affine connection
    (Springer US, 2015) Березовський, Володимир Євгенійович ; Berezovskii, V. E.
    This paper is devoted to the further development of the theory of almost geodesic mappings of spaces with affine connection.
  • 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 the first type of spaces with affine connection onto generalized 2-Ricci-symmetric spaces
    (Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 2021) Березовський, Володимир Євгенійович ; Лещенко, Світлана Валентинівна
    In the paper we consider almost geodesic mappings of the first type of spaces with affine connections onto generalized 2-Ricci-symmetric spaces. The main equations for the mappings are obtained as a closed system of linear differential equations of Cauchy type in the covariant derivatives. The obtained result extends an amount of research produced by Sinyukov, Berezovski and Mikeš.
  • Матеріал
    Canonical Almost Geodesic Mappings of the First Type of Spaces with Affine Connections onto Generalized m-Ricci-Symmetric Spaces
    (MDPI, 2021) Березовський, Володимир Євгенійович
    In the paper we consider almost geodesic mappings of the first type of spaces with affine connections onto generalized 2-Ricci-symmetric spaces, generalized 3-Ricci-symmetric spaces, and generalized m-Ricci-symmetric spaces. In either case the main equations for the mappings are obtained as a closed system of linear differential equations of Cauchy type in the covariant derivatives. The obtained results extend an amount of research produced by N.S. Sinyukov, V.E. Berezovski, J. Mikeš.
  • Матеріал
    Canonical Almost Geodesic Mappings of the First Type onto Generalized Ricci Symmetric Spaces
    (University of Nis, Serbia, 2022) Березовський, Володимир Євгенійович
    In the paper we consider canonical almost geodesic mappings of spaces with affine connection onto m-Ricci-symmetric spaces. In particular, we studied in detail canonical almost geodesic mappings of the first type of spaces with affine connections onto 2- and 3-Ricci-symmetric spaces. In either case the main equations for the mappings have been 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
    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
    Canonical F-Planar Mappings of Spaces with Affine Connection onto m-Symmetric Spaces
    (MDPI, 2023) Березовський, Володимир Євгенійович
    In this paper, we consider canonical F-planar mappings of spaces with affine connection onto m-symmetric spaces. We obtained the fundamental equations of these mappings in the form of a closed system of Chauchy-type equations in covariant derivatives. Furthermore, we established the number of essential parameters on which its general solution depends.
  • Матеріал
    Complex Submanifolds of LCK-manifold, Pseudo-Vaisman and Vaisman Manifolds
    (Slovak University of Technology in Bratislava, 2017) Березовський, Володимир Євгенійович
    Study the immersions of submanifolds in LCK-manifolds that a tangent space in all points of the submanifolds to be normal to Lee field and we find conditions under which LCK-manifold admits the immersion of complex submanifolds. Also we explore properties of Lee form of Vaisman and pseudo-Vaisman manifold.
  • Матеріал
    CONFORMAL AND GEODESIC MAPPINGS ONTO RICCI SYMMETRIC SPACES
    (Institute of Mathematics and Physics, SjF STU in Bratislava, 2020) Березовський, Володимир Євгенійович
    In this paper, we consider the conformal and geodesic mappings onto Ricci symmetric spaces. We obtained fundamental equations in the Cauchy type form, which depend on finite real parameters.
  • Матеріал
    Conformal and Geodesic Mappings onto Some Special Spaces
    (MDPI AG, Basel, Switzerland, 2019) Березовський, Володимир Євгенійович
    In this paper, we consider conformal mappings of Riemannian spaces onto Ricci-2-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-2-symmetric spaces. The main equations for the mappings are obtained as a closed system of Cauchy-type differential equations in covariant derivatives. We find the number of essential parameters which the solution of the system depends on. A similar approach was applied for the case of conformal mappings of Riemannian spaces onto Ricci-m-symmetric Riemannian spaces, as well as geodesic mappings of spaces with affine connections onto Ricci-m-symmetric spaces.
  • 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
    Conformal Mappings of Riemannian Spaces onto Ricci Symmetric Spaces
    (Pleiades Publishing, 2018) Березовський, Володимир Євгенійович
    In this paper consider conformal mappings of Riemannian spaces Vn onto Ricci symmetric Riemannian spaces. Note that Ricci symmetric spaces are characterized by the covariant constancy of the Ricci tensor; thereby, they are a natural generalization of Einstein spaces.
  • Матеріал
    Conharmonic Transformations of Locally Conformal Kahler Manifolds
    (Odessa National Academy of Food Technologies, 2021) Березовський, Володимир Євгенійович
  • Матеріал
    Diffeomorphism of affine connected spaces which preserved Riemannian and Ricci curvature tensors
    (Miskolc University Press, 2017) Березовський, Володимир Євгенійович
    In the present paper we study the preserving of Riemannian and Ricci tensors with respect to a diffeomorphism of spaces with affine connection. We consider geodesic and almost geodesic mappings of the first type. The basic equations of these maps form a closed system of Cauchy type in covariant derivatives. We determine the quantity of essential (substantial) parameters, on which depend the general solution of this problem.
  • 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.