Classification of Pseudo-Riemannian submersions with totally geodesic fibres from pseudo-hyperbolic spaces

TL;DR

This paper classifies certain geometric structures called pseudo-Riemannian submersions with totally geodesic fibres from pseudo-hyperbolic spaces, including cases with complex and para-complex structures, advancing understanding of their geometric properties.

Contribution

It provides a comprehensive classification of pseudo-Riemannian submersions with totally geodesic fibres from pseudo-hyperbolic spaces, including complex and para-complex cases.

Findings

Classification of submersions from real pseudo-hyperbolic spaces.

Classification of submersions with (para-)complex fibres.

Extension to pseudo-Riemannian manifolds with specific geometric structures.

Abstract

We classify pseudo-Riemannian submersions with connected totally geodesic fibres from a real pseudo-hyperbolic space onto a pseudo-Riemannian manifold. Also, we obtain the classification of the pseudo-Riemannian submersions with (para-)complex connected totally geodesic fibres from a (para-)complex pseudo-hyperbolic space onto a pseudo-Riemannian manifold.