Gray Curvature Identities for Almost Contact Metric Manifolds

TL;DR

This paper explores Gray curvature identities within almost contact metric manifolds, adapting concepts from almost hermitian manifolds using Boohby-Wang fibrations and warped manifolds to identify applicable curvature identities.

Contribution

It introduces a framework for establishing Gray curvature identities in almost contact manifolds, filling a gap in the geometric understanding of these structures.

Findings

Identifies potential Gray curvature identities for almost contact manifolds

Uses Boohby-Wang fibrations to relate almost contact and hermitian structures

Provides conditions under which these identities hold

Abstract

The aim of this research is the study of Gray curvature identities, introduced by Alfred Gray in \cite{kn:Gra76} for the class of almost hermitian manifolds. As known till now, there is no equivalent for the class of almost contact manifolds. For this purpose we use the Boohby-Wang fibration and the warped manifolds construction in order to establish which identities could be satisfied by an almost contact manifold.