Curvature identities on almost Hermitian manifolds and applications

TL;DR

This paper derives curvature identities for almost Hermitian manifolds, linking different connections, and applies these results to study the integrability and properties of special classes like quasi and nearly Kaehler manifolds.

Contribution

It systematically computes curvature and Bianchi identities for canonical and Levi-Civita connections on almost Hermitian manifolds, providing new insights into their geometric properties.

Findings

Derived curvature identities for canonical and Levi-Civita connections.

Established conditions for integrability of quasi Kaehler manifolds.

Explored properties of nearly Kaehler manifolds.

Abstract

In this paper, we systematically compute the Bianchi identities for the canonical connection on an almost Hermitian manifold. Moreover, we also compute the curvature tensor of the Levi-Civita connection on almost Hermitian manifolds in terms of curvature and torsion of the canonical connection. As applications of the curvature identities, we obtain some results about the integrability of quasi Kaehler manifolds and some properties of nearly Kaehler manifolds.