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.
Qi Zhang (1994)
Manuscripta mathematica
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S.-T. Yau, F. Zheng (1993)
Mathematische Zeitschrift
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Marco Brunella, Jorge Vitório Pereira, Frédéric Touzet (2006)
Bulletin de la Société Mathématique de France
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This paper is concerned with compact Kähler manifolds whose tangent bundle splits as a sum of subbundles. In particular, it is shown that if the tangent bundle is a sum of line bundles, then the manifold is uniformised by a product of curves. The methods are taken from the theory of foliations of (co)dimension 1.
Ken-ichi Sugiyama (1988)
Mathematische Annalen
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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 It will be reported, based on still unpublished papers of the author, that the Hartogs type extension theorem holds in the following two cases: 1) M is Kähler and ∂Ω is C²-smooth and not Levi flat; 2) M is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...
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.
Claude LeBrun, Simon Salamon (1994)
Inventiones mathematicae
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Jürgen Bingener (1983)
Mathematische Zeitschrift
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G. Tian (1987)
Inventiones mathematicae
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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...
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.