Displaying similar documents to “On Kähler metrics in lorentzian manifolds”

Selfdual Einstein hermitian four-manifolds

Vestislav Apostolov, Paul Gauduchon (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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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 ℍ P 2 and ℍ H 2 are hermitian.

Weakly-Einstein hermitian surfaces

Vestislav Apostolov, Oleg Muškarov (1999)

Annales de l'institut Fourier

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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 ℂ ℙ 2 ♯ ℂ ℙ ‾ 2 , ℂ ℙ 1 × ℂ ℙ 1 , and on the product surface X × Y of two curves X and Y whose genuses are greater than 1...