3-submersions from QR-hypersurfaces of quaternionic Kaehler manifolds

TL;DR

This paper investigates 3-submersions originating from QR-hypersurfaces in quaternionic Kähler manifolds and establishes the non-existence of certain quaternionic submersions between these manifolds.

Contribution

It introduces the study of 3-submersions from QR-hypersurfaces and proves a non-existence theorem for specific quaternionic submersions.

Findings

Non-existence of quaternionic submersions between non-hyper-Kähler quaternionic Kähler manifolds.

Characterization of 3-submersions from QR-hypersurfaces.

Insights into the structure of quaternionic Kähler manifolds.

Abstract

In this paper we study 3-submersions from a QR-hypersurface of a quaternionic Kaehler manifold onto an almost quaternionic hermitian manifold. We also prove the non-existence of quaternionic submersions between quaternionic Kaehler manifolds which are not locally hyper-Kaehler.