Curvature properties of pseudo-sphere bundles over paraquaternionic manifolds

TL;DR

This paper explores the curvature characteristics of twistor and reflector spaces over paraquaternionic Kähler manifolds and demonstrates the existence of mixed 3-Sasakian structures in certain principal bundles.

Contribution

It provides new curvature properties of twistor and reflector spaces and establishes the existence of mixed 3-Sasakian structures in SO(2,1)-bundles over paraquaternionic Kähler manifolds.

Findings

Curvature properties of twistor and reflector spaces are characterized.

Existence of positive and negative mixed 3-Sasakian structures is proven.

Results extend understanding of geometric structures over paraquaternionic Kähler manifolds.

Abstract

In this paper we obtain several curvature properties of the twistor and reflector spaces of a paraquaternionic K\"{a}hler manifold and prove the existence of both positive and negative mixed 3-Sasakian structures in a principal SO(2,1)-bundle over a paraquaternionic K\"{a}hler manifold.