Open AccessSpecial semi-reducible pseudo-Riemannian spaces
Author(s) -
Юлія Степанівна Федченко,
O. Lesechko
Publication year - 2021
Publication title -
trudy meždunarodnogo geometričeskogo centra/pracì mìžnarodnogo geometričnogo centru
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.124
H-Index - 2
eISSN - 2409-8906
pISSN - 2072-9812
DOI - 10.15673/tmgc.v14i1.1940
Subject(s) - mathematics , pure mathematics , ricci curvature , curvature of riemannian manifolds , riemann curvature tensor , topological tensor product , tensor (intrinsic definition) , scalar curvature , riemannian geometry , sign (mathematics) , metric tensor , mathematical analysis , sectional curvature , curvature , geometry , functional analysis , biochemistry , chemistry , gene , geodesic
The paper contains necessary conditions allowing to reduce matrix tensors of pseudo-Riemannian spaces to special forms called semi-reducible, under assumption that the tensor defining tensor characteristic of semireducibility spaces, is idempotent.
The tensor characteristic is reduced to the spaces of constant curvature, Ricci-symmetric spaces and conformally flat pseudo-Riemannian spaces.
The obtained results can be applied for construction of examples of spaces belonging to special types of pseudo-Riemannian spaces.
The research is carried out locally in tensor shape, without limitations imposed on a sign of a metric.