Conformal semi-invariant submersions

TL;DR

This paper introduces conformal semi-invariant submersions from almost Hermitian to Riemannian manifolds, exploring their geometric properties, product structures, harmonicity, and conditions for total geodesicity.

Contribution

It generalizes semi-invariant submersions by defining conformal variants and investigates their geometric and harmonic properties in detail.

Findings

Existence of certain product structures on the total space

Conditions for harmonicity of conformal semi-invariant submersions

Necessary and sufficient conditions for total geodesicity

Abstract

As a generalization of semi-invariant submersions, we introduce conformal semi-invariant submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations which are arisen from the definition of a conformal submersion and show that there are certain product structures on the total space of a conformal semi-invariant submersion. Moreover, we also check the harmonicity of such submersions and find necessary and sufficient conditions of a conformal semi-invariant submersion to be totally geodesic.