H-anti-invariant submersions from almost quaternionic Hermitian manifolds

TL;DR

This paper introduces and studies h-anti-invariant and h-Lagrangian submersions from almost quaternionic Hermitian manifolds, exploring their properties, conditions for harmonicity, and geometric decompositions.

Contribution

It generalizes existing submersion concepts and provides new characterizations, conditions, and examples for these generalized maps.

Findings

Characterization of integrability of distributions

Conditions for harmonicity of submersions

Decomposition theorems for the manifolds

Abstract

As a generalization of anti-invariant Riemannian submersions and Lagrangian Riemannian submersions, we introduce the notions of h-anti-invariant submersions and h-Lagrangian submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds. We obtain characterizations and investigate some properties: the integrability of distributions, the geometry of foliations, and the harmonicity of such maps. We also find a condition for such maps to be totally geodesic and give some examples of such maps. Finally, we obtain some types of decomposition theorems.