Displaying similar documents to “Holomorphic Cartan geometries and rational curves”

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 It will be reported, based on still unpublished papers of the author, that the Hartogs type extension theorem holds in the following two cases: 1) M is Kähler and ∂Ω is C²-smooth and not Levi flat; 2) M is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...

QCH Kähler manifolds with κ = 0

Włodzimierz Jelonek (2014)

Colloquium Mathematicae

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The aim of this paper is to describe all Kähler manifolds with quasi-constant holomorphic sectional curvature with κ = 0.

Kähler manifolds of quasi-constant holomorphic sectional curvatures

Georgi Ganchev, Vesselka Mihova (2008)

Open Mathematics

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The Kähler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kähler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the geometric angle, associated with the section. A curvature identity characterizing such manifolds is found. The biconformal group of transformations whose elements transform Kähler metrics into Kähler ones is introduced and biconformal tensor invariants...

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...

Two remarks on Kähler homogeneous manifolds

Bruce Gilligan, Karl Oeljeklaus (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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We prove that every Kähler solvmanifold has a finite covering whose holomorphic reduction is a principal bundle. An example is given that illustrates the necessity, in general, of passing to a proper covering. We also answer a stronger version of a question posed by Akhiezer for homogeneous spaces of nonsolvable algebraic groups in the case where the isotropy has the property that its intersection with the radical is Zariski dense in the radical.