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.
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.
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...
Claude LeBrun, Simon Salamon (1994)
Inventiones mathematicae
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S.-T. Yau, F. Zheng (1993)
Mathematische Zeitschrift
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Zbigniew Olszak (2003)
Colloquium Mathematicae
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It is proved that there exists a non-semisymmetric pseudosymmetric Kähler manifold of dimension 4.
John S. Bland (1985)
Inventiones mathematicae
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Lucia Alessandrini, Marco Andreatta (1987)
Compositio Mathematica
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G. Tian (1987)
Inventiones mathematicae
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Zbigniew Olszak (1984)
Banach Center Publications
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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.
Le Mau Hai, Nguyen Van Khue, Pham Hoang Hiep (2007)
Annales Polonici Mathematici
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We establish some results on ω-pluripolarity and complete ω-pluripolarity for sets in a compact Kähler manifold X with fundamental form ω. Moreover, we study subextension of ω-psh functions on a hyperconvex domain in X and prove a comparison principle for the class 𝓔(X,ω) recently introduced and investigated by Guedj-Zeriahi.
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...
Włodzimierz Jelonek (2012)
Colloquium Mathematicae
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The aim of this paper is to present examples of holomorphically pseudosymmetric Kähler metrics on the complex projective spaces ℂℙⁿ, where n ≥ 2.
Simone Calamai, David Petrecca (2017)
Complex Manifolds
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In this short note, we prove that a Calabi extremal Kähler-Ricci soliton on a compact toric Kähler manifold is Einstein. This settles for the class of toric manifolds a general problem stated by the authors that they solved only under some curvature assumptions.
R. Goto (1994)
Geometric and functional analysis
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Koji Matsuo (2009)
Colloquium Mathematicae
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We show that there exist astheno-Kähler structures on Calabi-Eckmann manifolds.
Jürgen Bingener (1983)
Mathematische Zeitschrift
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Michela Zedda (2017)
Complex Manifolds
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In this paper we study Kähler manifolds that are strongly not relative to any projective Kähler manifold, i.e. those Kähler manifolds that do not share a Kähler submanifold with any projective Kähler manifold even when their metric is rescaled by the multiplication by a positive constant. We prove two results which highlight some relations between this property and the existence of a full Kähler immersion into the infinite dimensional complex projective space. As application we get that...
Ngaiming Mok (1997)
Journal für die reine und angewandte Mathematik
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