SPACE, TIME AND FUNDAMENTAL INTERACTIONS

$H$-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}.