Isometry groups of Lobachevskian spaces, similarity transformation groups of Euclidean spaces and Lorentzian holonomy groups

Abstract

Weakly-irreducible not irreducible subalgebras of $\so(1,n+1)$ were classified by L. Berard Bergery and A. Ikemakhen. In the present paper a geometrical proof of this result is given. Transitively acting isometry groups of Lobachevskian spaces and transitively acting similarity transformation groups of Euclidean spaces are classified.

arXiv comment12 pages

References in corpus (1)

• The spaces of curvature tensors for holonomy algebras of Lorentzian manifolds

Cited by in corpus (4)

• Metrics that realize all Lorentzian holonomy algebras
• Holonomy groups and special geometric structures of pseudo-Kählerian manifolds of index 2
• Classification of connected holonomy groups of pseudo-Kählerian manifolds of index 2
• Note on the holonomy groups of pseudo-Riemannian manifolds