Some integrability conditions for almost Kähler manifolds

Abstract

Among other results, a compact almost Kähler manifold is proved to be Kähler 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 Kähler manifolds with harmonic Weyl tensor and non-parallel semi-positive Ricci tensor. Stronger results are obtained in dimension 4.

Latex2e, 13 pages

References in corpus (1)

• A splitting theorem for Kahler manifolds whose Ricci tensors have constant eigenvalues

Cited by in corpus (5)

• Gray identities, canonical connection and integrability
• Einstein Metrics, Harmonic Forms, and Symplectic Four-Manifolds
• Integrability Conditions For Almost Hermitian And Almost Kaehler 4-Manifolds
• Symplectic curvature flow revisited
• Relating the curvature tensor and the complex Jacobi operator of an almost Hermitian manifold