Corpus ID: 15803265

Integrability Conditions For Almost Hermitian And Almost Kaehler 4-Manifolds

@article{Kirchberg2006IntegrabilityCF,
  title={Integrability Conditions For Almost Hermitian And Almost Kaehler 4-Manifolds},
  author={K. Kirchberg},
  journal={arXiv: Differential Geometry},
  year={2006}
}
  • K. Kirchberg
  • Published 2006
  • Mathematics
  • arXiv: Differential Geometry
  • If $W_+$ denotes the self dual part of the Weyl tensor of any K\"ahler 4-manifold and $S$ its scalar curvature, then the relation $|W_+|^2 = S^2/6$ is well-known. For any almost K\"ahler 4-manifold with $S \ge 0$, this condition forces the K\"ahler property. A compact almost K\"ahler 4-manifold is already K\"ahler if it satisfies the conditions $| W_+ |^2 = S^2/6$ and $\delta W_+=0$ and also if it is Einstein and $| W_+|$ is constant. Some further results of this type are proved. An almost… CONTINUE READING
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