Generic Riemannian submersions from nearly Kaehler manifolds

TL;DR

This paper explores the geometric properties of generic Riemannian submersions from nearly Kaehler manifolds, focusing on integrability, geodesic conditions, and harmonicity to deepen understanding of their structure.

Contribution

It provides new conditions for integrability, geodesic leaves, totally geodesic maps, and harmonic maps in the context of Riemannian submersions from nearly Kaehler manifolds.

Findings

Conditions for integrability of distributions

Criteria for leaves to be totally geodesic

Conditions for submersions to be harmonic maps

Abstract

We study generic Riemannian submersions from nearly Kaehler manifolds onto Riemannian manifolds. We investigate conditions for the integrability of various distributions arising for generic Riemannian submersions and also obtain conditions for leaves to be totally geodesic foliations. We obtain conditions for a generic Riemannian submersion to be a totally geodesic map and also study generic Riemannian submersions with totally umbilical fibers. Finally, we derive conditions for generic Riemannian submersions to be harmonic map.