Curvature identities on almost Hermitian manifolds and applications
Differential Geometry
2018-12-14 v2
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.
Keywords
Cite
@article{arxiv.1209.5642,
title = {Curvature identities on almost Hermitian manifolds and applications},
author = {Chengjie Yu},
journal= {arXiv preprint arXiv:1209.5642},
year = {2018}
}
Comments
15 pages, a mistake in the published version in Theorem 3.5 was fixed