Homogeneous pseudo-Riemannian structures of metrics of Kaluza-Klein type on the three-dimensional anti-de Sitter spacetime

Abstract

We classify homogeneous pseudo-Riemannian structures of a three-parameter family of metrics called Kaluza-Klein type on the three-dimensional anti-de Sitter spacetime with their induced groups of isometries and reductive decompositions. We also obtain the classification of homogeneous almost contact and paracontact metric structures of metrics of Kaluza-Klein type on the three-dimensional anti-de Sitter spacetime with their isometry groups and reductive decompositions.

36 pages. v3: Minor revision. The erroneous existence statement corrected in v2 (Theorem 4.6 and Theorem 5.3; Theorem 5.4 in v2) remains corrected. Lemma 5.2 has been removed as unnecessary, and the numbering has been updated accordingly. Main results unchanged