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2019, no. 4


Aminova A.V., Khakimov D.R.

In this paper we study five-dimensional \(h\)-spaces (\(H_{41}\), \(g\)) of type {41} [4]. Necessary and sufficient conditions for (\(H_{41}\), \(g\)) to be a space of constant curvature are found. The general solution of the Eisnhart equation in \(h\)-space (\(H_{41}\), \(g\)) of non-constant curvature is determined. We establish conditions for the existence of a non-homothetic projective motion in (\(H_{41}\), \(g\)) and describe the structure of a non-homothetic projective Lie algebra in \(h\)-space (\(H_{41}\), \(g\)) of type {41}.

Keywords: five-dimensional pseudo-Riemannian manifold, \(h\)-space of type {41}, Eisenhart equation, projective Lie algebra.

UDC: 514.763, 512.816

PACS: 04.50.+h, 04.50.-h, 02.40-k, 02.20.Sv

DOI: 10.17238/issn2226-8812.2019.4.4-12

Please cite this article in English as:
Aminova A. V., Khakimov D. R. \(H\)-spaces (\(H_{41}\), \(g\)) of type {41}: projective-group properties. Space, Time and Fundamental Interactions, 2019, no. 4, pp. 4-12.