Some integrability conditions for almost K\"ahler manifolds
Differential Geometry
2015-06-26 v1
Abstract
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.
Cite
@article{arxiv.math/0304092,
title = {Some integrability conditions for almost K\"ahler manifolds},
author = {Klaus-Dieter Kirchberg},
journal= {arXiv preprint arXiv:math/0304092},
year = {2015}
}
Comments
Latex2e, 13 pages