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Weakly-Einstein hermitian surfaces

Vestislav ApostolovOleg Muškarov — 1999

Annales de l'institut Fourier

A consequence of the Riemannian Goldberg-Sachs theorem is the fact that the Kähler form of an Einstein Hermitian surface is an eigenform of the curvature operator. Referring to this property as we obtain a complete classification of the compact locally homogeneous * -Einstein Hermitian surfaces. We also provide large families of non-homogeneous * -Einstein (but non-Einstein) Hermitian metrics on 2 2 , 1 × 1 , and on the product surface X × Y of two curves X and Y whose genuses are greater than 1 and 0, respectively....

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