On the existence of proper Nearly Kenmotsu manifolds

TL;DR

This paper explores the properties of nearly Kenmotsu manifolds, establishing their local isometry to warped products with nearly Kähler manifolds and proving the non-existence of certain hypersurfaces.

Contribution

It provides new results on nearly Kenmotsu manifolds, including their local structure and the non-existence of nearly Kenmotsu hypersurfaces in nearly Kähler manifolds.

Findings

Nearly Kenmotsu manifolds are locally isometric to warped products of real line and nearly Kähler manifolds.

No nearly Kenmotsu hypersurfaces exist in nearly Kähler manifolds.

Normal nearly Kenmotsu manifolds are shown to be Kenmotsu manifolds.

Abstract

This is an expository paper, which provides a first approach to nearly Kenmotsu manifolds. The purpose of this paper is to focus on nearly Kenmotsu manifolds and get some new results from it. We prove that for a nearly Kenmotsu manifold is locally isometric to warped product of real line and nearly K\"ahler manifold. Finally, we prove that there exist no nearly Kenmotsu hypersurface of nearly K\"ahler manifold. It is shown that a normal nearly Kenmotsu manifold is Kenmotsu manifold.