Almost h-conformal semi-invariant submersions from almost quaternionic Hermitian manifolds

TL;DR

This paper introduces and studies a new class of maps called h-conformal semi-invariant submersions from almost quaternionic Hermitian manifolds to Riemannian manifolds, exploring their geometric properties and providing examples.

Contribution

It defines h-conformal semi-invariant submersions and analyzes their geometric properties, extending the theory of submersions in differential geometry.

Findings

Conditions for foliations to be integrable

Criteria for total manifolds to be locally product spaces

Characterizations of totally geodesic maps

Abstract

As a generalization of Riemannian submersions, horizontally conformal submersions, semi-invariant submersions, h-semi-invariant submersions, almost h-semi-invariant submersions, conformal semi-invariant submersions, we introduce h-conformal semi-invariant submersions and almost h-conformal semi-invariant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds. We study their properties: the geometry of foliations, the conditions for total manifolds to be locally product manifolds, the conditions for such maps to be totally geodesic, etc. Finally, we give some examples of such maps.