摘要
We systematically derive 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 K¨ahler manifolds and nearly K¨ahler manifolds.
We systematically derive 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 Kahler manifolds and nearly Kahler manifolds.
基金
supported by Science Foundation of Guangdong Province (Grant No. S2012010010038)
National Natural Science Foundation of China (Grant No. 11571215)
supporting project from the Department of Education of Guangdong Province (Grant No. Yq2013073)
