Almost h-semi-slant Riemannian maps

TL;DR

This paper introduces almost h-semi-slant Riemannian maps from quaternionic Hermitian to Riemannian manifolds, exploring their geometric properties, integrability, harmonicity, and conditions for being totally geodesic, with illustrative examples.

Contribution

It defines a new class of Riemannian maps generalizing several existing concepts and investigates their fundamental geometric properties and conditions.

Findings

Conditions for integrability of distributions

Criteria for harmonicity of the maps

Characterization of totally geodesic maps

Abstract

As a generalization of slant Riemannian maps (Sahin), semi-slant Riemannian maps (Park), almost h-slant submersions (Park 2012), and almost h-semi-slant submersions (Park 2011), we introduce the notion of almost h-semi-slant Riemannian maps from almost quaternionic Hermitian manifolds to Riemannian manifolds. We investigate the integrability of distributions, the harmonicity of such maps, the geometry of fibers, etc. We also deal with the condition for such maps to be totally geodesic and study some decomposition theorems. Moreover, we give some examples.