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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....

Selfdual Einstein hermitian four-manifolds

Vestislav ApostolovPaul Gauduchon — 2002

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We provide a local classification of selfdual Einstein riemannian four-manifolds admitting a positively oriented hermitian structure and characterize those which carry a hyperhermitian, non-hyperkähler structure compatible with the negative orientation. We show that selfdual Einstein 4-manifolds obtained as quaternionic quotients of P 2 and H 2 are hermitian.

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