Holomorphic group actions with few compact orbits
Christoph Gellhaus, Tilmann Wurzbacher (2001)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Christoph Gellhaus, Tilmann Wurzbacher (2001)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Włodzimierz Jelonek (2009)
Colloquium Mathematicae
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The aim of this paper is to present the first examples of compact, simply connected holomorphically pseudosymmetric Kähler manifolds.
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 for some unitary representation . By our earlier work there exists a -closed holomorphic 1-form with coefficients twisted by some unitary representation , possibly non-isomorphic to . Taking norms we obtains...
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.
Lucia Alessandrini, Marco Andreatta (1987)
Compositio Mathematica
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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 It will be reported, based on still unpublished papers of the author, that the Hartogs type extension theorem holds in the following two cases: 1) M is Kähler and ∂Ω is C²-smooth and not Levi flat; 2) M is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...
John S. Bland (1985)
Inventiones mathematicae
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Ngaiming Mog (1986)
Mathematische Zeitschrift
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Terence Napier, Mohan Ramachandran (1997)
Annales de l'institut Fourier
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It is proved that if is a weakly 1-complete Kähler manifold with only one end, then or there exists a proper holomorphic mapping of onto a Riemann surface.