All Issues

2019, no. 1

ON PROJECTIVE MOTIONS OF 5-DIMENSIONAL SPACES II. H-SPACES OF THE TYPE {41}

Aminova A.V., Khakimov D.R.

We study five-dimensional pseudo-Riemannian manifolds (M,g) that admit non-homothetic infinitesimal projective transformations. A similar problem for n-dimensional proper Riemannian and Lorentzian spaces was solved by T. Levi-Civita, A.Z. Petrov, A.S. Solodovnikov, and A.V. Aminova. For pseudo-Riemannian manifolds of arbitrary signature and dimension the problem of their classification on algebras and Lie groups of projective transformations, set over a hundred years ago, remains open. In this paper, using the method of the skew-normal frame (Aminova), five-dimensional h-spaces of type {41} are defined and necessary and sufficient conditions for the existence of projective motions of the same type are established.

Keywords: five-dimensional pseudo-Riemannian manifold, projective motion, h-space of the type {41}.

UDC: 514.763: 514.8

PACS: 11.10.Kk

DOI: 10.17238/issn2226-8812.2019.1.45-55

Please cite this article in English as:
Aminova A.V., Khakimov D.R. On projective motions of 5-dimensional spaces II. h-spaces of the type {41}. Space, Time and Fundamental Interactions, 2019, no. 1, pp. 45-55.