All Issues
PROJECTIVE-GROUP PROPERTIES OF \(H\)-SPACES \(H_{5}\) OF TYPE
Aminova A.V., Khakimov D.R.
The five-dimensional \(h\)-spaces \(H_{5}\) of type {5} [3] are studied. Necessary and sufficient conditions for \(H_{5}\) to be a space of constant curvature are found. The general solution of the Eisenhart equation in \(h\)-space \(H_{5}\) of non-constant curvature is determined. The conditions for the existence of a non-homothetic projective motion in \(H_{5}\) are established, and the structure of a non-homothetic projective Lie algebra in \(h\)-space \(H_{5}\) of type {5} is described.
Keywords: five-dimensional pseudo-Riemannian manifold, rigid \(h\)-space \(H_{5}\) of type {5}, Eisenhart equation, projective motion.
UDC: 514.763, 514.8
PACS: 11.10.Kk, 04.50.+h, 04.50.-h, 02.40-k, 02.20.Sv
DOI: 10.17238/issn2226-8812.2020.1.4-11
Please cite this article in English as:
Aminova A.V., Khakimov D.R. Projective-group properties of \(H\)-spaces \(H_{5}\) of type {5}. Space, Time and Fundamental Interactions, 2020, no. 1, pp. 4-11.