On bi-slant submersions in complex geometry

TL;DR

This paper introduces bi-slant submersions from almost Hermitian manifolds to Riemannian manifolds, generalizing several existing submersion types, and explores their geometric properties, curvature relations, and examples.

Contribution

It defines bi-slant submersions from almost Hermitian manifolds, especially Kaehler manifolds, and investigates their geometric structure and curvature relations, extending prior concepts.

Findings

Provided a proper example of bi-slant submersion.

Analyzed the geometry of foliations and leaves.

Derived curvature relations between manifolds.

Abstract

In the present paper, we introduce bi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalization of invariant, anti-invariant, semi-invariant, slant, semi-slant and hemi-slant Riemannian submersions. We mainly focus on bi-slant submersions from Kaehler manifolds. We provide a proper example of bi-slant submersion, investigate the geometry of foliations determined by vertical and horizontal distributions, and obtain the geometry of leaves of these distributions. Moreover, we obtain curvature relations between the base space, the total space and the fibres, and find geometric implications of these relations.