Abstract:
We study 5-dimensional pseudo-Riemannian manifolds in the form of $h$-spaces $H_{32}$ of type $\{32\}$. A classification of $h$-spaces $H_{32,2}$ is given according to (non-homothetic) Lie algebras of infinitesimal projective and affine transformations, all projectively mobile metrics are found and the dimensions, basis elements and structural equations of the maximal non-homothetic projective Lie algebras operating in them are indicated.
Keywords:5-dimensional pseudo-Riemannian manifold, $h$-space $H_ {32,2}$ of type $\{32\}$, system of partial differential equations, non-homothetical projective motion, Killing equation, projective Lie algebra.
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