Open AccessInvestigation of conformally killing vector fields on 5-dimensional 2-symmetric lorentzian manifolds
Author(s) -
Tatiana Andreeva,
D. N. Oskorbin,
E. D. Rodionov
Publication year - 2021
Publication title -
vestnik ûgorskogo gosudarstvennogo universiteta
Language(s) - English
Resource type - Journals
eISSN - 2078-9114
pISSN - 1816-9228
DOI - 10.17816/byusu20210117-22
Subject(s) - indecomposable module , killing vector field , mathematics , vector field , pure mathematics , ricci flat manifold , riemannian geometry , homogeneous , curvature of riemannian manifolds , class (philosophy) , mathematical analysis , sectional curvature , geometry , scalar curvature , combinatorics , computer science , curvature , artificial intelligence
Conformally Killing fields play an important role in the theory of Ricci solitons and also generate an important class of locally conformally homogeneous (pseudo) Riemannian manifolds. In the Riemannian case, V. V. Slavsky and E.D. Rodionov proved that such spaces are either conformally flat or conformally equivalent to locally homogeneous Riemannian manifolds. In the pseudo-Riemannian case, the question of their structure remains open. Pseudo-Riemannian symmetric spaces of order k, where k 2, play an important role in research in pseudo-Riemannian geometry. Currently, they have been investigated in cases k=2,3 by D.V. Alekseevsky, A.S. Galaev and others. For arbitrary k, non-trivial examples of such spaces are known: generalized Kachen - Wallach manifolds. In the case of small dimensions, these spaces and Killing vector fields on them were studied by D.N. Oskorbin, E.D. Rodionov, and I.V. Ernst with the helpof systems of computer mathematics. In this paper, using the Sagemath SCM, we investigate conformally Killing vector fields on five-dimensional indecomposable 2- symmetric Lorentzian manifolds, and construct an algorithm for their computation.