INFINITESIMAL CONFORMAL TRANSFORMATIONS OF RIEMANNIAN MANIFOLDS WHICH PRESERVE THE GENERALIZED EINSTEIN TENSOR
INFINITESIMAL CONFORMAL TRANSFORMATIONS OF RIEMANNIAN MANIFOLDS WHICH PRESERVE THE GENERALIZED EINSTEIN TENSOR
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Дата
2020
Автори
Березовський, Володимир Євгенійович
Ненька, Руслана Володимирівна
Лещенко, Світлана Валентинівна
Назва журналу
ISSN журналу
Назва тома
Видавець
Institute of Mathematics and Physics, SjF STU in Bratislava
Інструкція
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.
Опис
Ключові слова
affine connection,
Riemannian manifolds,
generalized Einstein tensor,
con- formal transformation,
Lie derivative
Бібліографічний опис
CHEREVKO Y., BEREZOVSKII V., NENKA R., LESHCHENKO S. INFINITESIMAL CONFORMAL TRANSFORMATIONS OF RIEMANNIAN MANIFOLDS WHICH PRESERVE THE GENERALIZED EINSTEIN TENSOR \\ Proceedigs 19th Conference on Applied Mathematics APLIMAT 2020, PP. 244-252