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- W1495267251 abstract "If $W_+$ denotes the self dual part of the Weyl tensor of any Kahler 4-manifold and $S$ its scalar curvature, then the relation $|W_+|^2 = S^2/6$ is well-known. For any almost Kahler 4-manifold with $S ge 0$, this condition forces the Kahler property. A compact almost Kahler 4-manifold is already Kahler 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 Hermitian 4-manifold $(M,g,J)$ with $mathrm{supp} (W_+)=M$ is already Kahler if it satisfies the condition $| W_+ |^2 = 3 (S_{star} - S/3)^2 /8$ together with $|nabla W_+ | = | nabla |W_+||$ or with $delta W_+ + nabla log | W_+ | lrcorner W_+ =0$, respectively. The almost complex structure $J$ enters here explicitely via the star scalar curvature $S_{star}$ only." @default.
- W1495267251 created "2016-06-24" @default.
- W1495267251 creator A5029314392 @default.
- W1495267251 date "2006-05-23" @default.
- W1495267251 modified "2023-09-27" @default.
- W1495267251 title "Integrability Conditions For Almost Hermitian And Almost Kaehler 4-Manifolds" @default.
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