Some integrability conditions for almost Kähler manifolds

✍ Scribed by K.-D. Kirchberg

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 125 KB
• Volume: 49
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(03)00085-8

✦ Synopsis

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.