On the existence of bounded holomorphic functions on complete Kähler manifolds.
John S. Bland (1985)
Inventiones mathematicae
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John S. Bland (1985)
Inventiones mathematicae
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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.
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.
Thomas Fiedler (1988)
Mathematische Annalen
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S.-T. Yau, F. Zheng (1993)
Mathematische Zeitschrift
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Claude LeBrun, Simon Salamon (1994)
Inventiones mathematicae
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Lucia Alessandrini, Marco Andreatta (1987)
Compositio Mathematica
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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.
Koji Matsuo, Takao Takahashi (2001)
Colloquium Mathematicae
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We prove that every compact balanced astheno-Kähler manifold is Kähler, and that there exists an astheno-Kähler structure on the product of certain compact normal almost contact metric manifolds.
R. Goto (1994)
Geometric and functional analysis
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Ngaiming Mog (1986)
Mathematische Zeitschrift
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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...
Ngaiming Mok (1997)
Journal für die reine und angewandte Mathematik
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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.