SOME EXAMPLES OF HERMITIAN SURFACES

초록

The Riemannian version of the Goldberg-Sachs theorem says that a compact Einstein Hermitian surface is locally conformal Kahler. In contrast to the compact case, we show that there exists an Einstein Hermitian surface which is not locally conformal Kahler. On the other hand, it is known that on a compact Hermitian surface M-4, the zero scalar curvature defect implies that M-4 is Kahler. Contrary to the compact case, we show that there exists a non-Kahler Hermitian surface with zero scalar curvature defect.

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