Abstract
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 Kähler manifolds and nearly Kähler manifolds.
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Acknowledgements
This work was supported by Science Foundation of Guangdong Province (Grant No. S2012010010038), National Natural Science Foundation of China (Grant No. 11571215) and a supporting project from the Department of Education of Guangdong Province (Grant No. Yq2013073). The author thanks the referees for the helpful and inspiring suggestions.
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Yu, C. Curvature identities on almost Hermitian manifolds and applications. Sci. China Math. 60, 285–300 (2017). https://doi.org/10.1007/s11425-016-0022-6
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DOI: https://doi.org/10.1007/s11425-016-0022-6