Some integrability conditions for almost Kähler manifolds

Details Some integrability conditions for almost Kähler manifolds Some integrability conditions for almost Kähler manifolds

2003-04-07

arxiv.org/abs/math/0304092v1

Mathematics

Differential Geometry

Latex2e, 13 pages

Scientific paper

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.

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