2019, no. 4

### $$H$$-SPACES ($$H_{41}$$, $$g$$) OF TYPE {41}: PROJECTIVE-GROUP PROPERTIES

#### 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

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.