On H-Conformal Semi-invariant Submersion

TL;DR

This paper studies special types of geometric mappings called h-conformal semi-invariant submersions from quaternionic Kähler manifolds to Riemannian manifolds, analyzing their properties, conditions for being totally geodesic, and their relation to twisted product structures.

Contribution

It introduces and characterizes h-conformal semi-invariant submersions, providing conditions for their geometric properties and examples from quaternionic Kähler manifolds.

Findings

Conditions for submersions to be totally geodesic.

Characterization of when the total manifold is a twisted product.

Examples illustrating the theory.

Abstract

We explore h-conformal semi-invariant submersions and almost h-conformal semi-invariant submersions originating from quaternionic K\"ahler manifolds to Riemannian manifolds. Our investigation focuses on the geometric characteristics of these submersions, including the integrability of distributions and the geometry of foliations. Additionally, we establish the necessary and sufficient conditions for such submersions to be totally geodesic. We also examine the equivalent conditions for the total manifold of the submersion to be twisted product manifold. Finally, we present a series of examples illustrating quaternionic K\"ahler manifolds and h-conformal semi-invariant submersions from quaternionic K\"ahler manifolds to Riemannian manifolds.