2020, no. 1

### 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.