Displaying similar documents to “Selfdual Einstein hermitian four-manifolds”

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...

The Dolbeault operator on Hermitian spin surfaces

Bodgan Alexandrov, Gueo Grantcharov, Stefan Ivanov (2001)

Annales de l’institut Fourier

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We prove the vanishing of the kernel of the Dolbeault operator of the square root of the canonical line bundle of a compact Hermitian spin surface with positive scalar curvature. We give lower estimates of the eigenvalues of this operator when the conformal scalar curvature is non -negative.

Einstein-Hermitian and anti-Hermitian 4-manifolds

Włodzimierz Jelonek (2003)

Annales Polonici Mathematici

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We study 4-dimensional Einstein-Hermitian non-Kähler manifolds admitting a certain anti-Hermitian structure. We also describe Einstein 4-manifolds which are of cohomogeneity 1 with respect to an at least 4-dimensional group of isometries.

An anti-Kählerian Einstein structure on the tangent bundle of a space form

Vasile Oproiu, Neculai Papaghiuc (2005)

Colloquium Mathematicae

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In [11] we have considered a family of almost anti-Hermitian structures (G,J) on the tangent bundle TM of a Riemannian manifold (M,g), where the almost complex structure J is a natural lift of g to TM interchanging the vertical and horizontal distributions VTM and HTM and the metric G is a natural lift of g of Sasaki type, with the property of being anti-Hermitian with respect to J. Next, we have studied the conditions under which (TM,G,J) belongs to one of the eight classes of anti-Hermitian...