On paraquaternionic submersions between paraquaternionic K\"ahler manifolds

TL;DR

This paper investigates properties of semi-Riemannian submersions between paraquaternionic K"ahler manifolds, establishing non-existence results and analyzing the tangent bundle's canonical projection with Sasaki metric.

Contribution

It proves the non-existence of certain paraquaternionic submersions and examines the tangent bundle's canonical projection in this geometric context.

Findings

Non-existence of paraquaternionic submersions between specific manifolds

Analysis of the tangent bundle with Sasaki metric

Characterization of paraquaternionic structures in submersion contexts

Abstract

In this paper we deal with some properties of a class of semi-Riemannian submersions between manifolds endowed with paraquaternionic structures, proving a result of non-existence of paraquaternionic submersions between paraquaternionic K\"ahler non locally hyper paraK\"ahler manifolds. Then we examine, as an example, the canonical projection of the tangent bundle, endowed with the Sasaki metric, of an almost paraquaternionic Hermitian manifold.