March 3, 2026

Lie Algebras of Projective Motions of h-spaces H32, 2 of the Type 32

Key Points

The research identifies the structure of maximal nonhomothetic projective Lie algebras within 5-dimensional pseudo-Riemannian manifolds.
A classification of h-spaces H32,2 reveals the dimensions and basis elements of relevant Lie algebras for projective transformations.
Analysis of projectively mobile metrics shows how various transformation types influence the manifold's geometry.
This work supports understanding of transformation symmetries in pseudo-Riemannian spaces, enhancing geometric theory.

Abstract

5-dimensional pseudo-Riemannian manifolds in the form of h-spaces H32 of the type 32 are considered. A classification of h-spaces H32, 2 with respect to (nonhomothetic) Lie algebras of infinitesimal projective and affine transformations is given, all projectively mobile metrics are found, and the dimensions, basis elements and structural equations of the maximal nonhomothetic projective Lie algebras operating in them are indicated.

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Lie Algebras of Projective Motions of h-spaces H32, 2 of the Type 32

Key Points

Abstract

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