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Displaying similar documents to “Two remarks on Kähler homogeneous manifolds”

Fibrations of compact Kähler manifolds in terms of cohomological properties of their fundamental groups

Ngaiming Mok (2000)

Annales de l'institut Fourier

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We prove fibration theorems on compact Kähler manifolds with conditions on first cohomology groups of fundamental groups with respect to unitary representations into Hilbert spaces. If the fundamental group T of compact Kähler manifold X violates Property (T) of Kazhdan’s, then H 1 ( G a m m a , Φ ) ≠ 0 for some unitary representation Φ . By our earlier work there exists a d -closed holomorphic 1-form with coefficients twisted by some unitary representation Φ ' , possibly non-isomorphic to Φ . Taking norms we obtains...

Holomorphic Cartan geometries and rational curves

Indranil Biswas, Benjamin McKay (2016)

Complex Manifolds

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We prove that any compact Kähler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact Kähler manifold. This shows that many complex manifolds admit no or few holomorphic Cartan geometries.

Hartogs type extension theorems on some domains in Kähler manifolds

Takeo Ohsawa (2012)

Annales Polonici Mathematici

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Given a locally pseudoconvex bounded domain Ω, in a complex manifold M, the Hartogs type extension theorem is said to hold on Ω if there exists an arbitrarily large compact subset K of Ω such that every holomorphic function on Ω-K is extendible to a holomorphic function on Ω. It will be reported, based on still unpublished papers of the author, that the Hartogs type extension theorem holds in the following two cases: 1) M is Kähler and ∂Ω is C²-smooth and not Levi flat; 2) M is compact...