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arXiv:math/0304092 [math.DG]AbstractReferencesReviewsResources

Some integrability conditions for almost Kähler manifolds

Klaus-Dieter Kirchberg

Published 2003-04-07Version 1

Among other results, a compact almost K\"ahler manifold is proved to be K\"ahler if the Ricci tensor is semi-negative and its length coincides with that of the star Ricci tensor or if the Ricci tensor is semi-positive and its first order covariant derivatives are Hermitian. Moreover, it is shown that there are no compact almost K\"ahler manifolds with harmonic Weyl tensor and non-parallel semi-positive Ricci tensor. Stronger results are obtained in dimension 4.

Comments: Latex2e, 13 pages
Categories: math.DG
Subjects: 53B20, 53C25
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