Fibrations of compact Kähler manifolds in terms of cohomological properties of their fundamental groups

Ngaiming Mok

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Displaying similar documents to “Fibrations of compact Kähler manifolds in terms of cohomological properties of their fundamental groups”

The Bochner-Hartogs dichotomy for weakly 1-complete Kähler manifolds

Terence Napier, Mohan Ramachandran (1997)

Annales de l'institut Fourier

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It is proved that if $M$ is a weakly 1-complete Kähler manifold with only one end, then $H_{c}^{1} (M, 𝒪) = 0$ or there exists a proper holomorphic mapping of $M$ onto a Riemann surface.

On holomorphic maps into compact non-Kähler manifolds

Masahide Kato, Noboru Okada (2004)

Annales de l’institut Fourier

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We study the extension problem of holomorphic maps $σ : H \to X$ of a Hartogs domain $H$ with values in a complex manifold $X$ . For compact Kähler manifolds as well as various non-Kähler manifolds, the maximal domain $Ω_{σ}$ of extension for $σ$ over $Δ$ is contained in a subdomain of $Δ$ . For such manifolds, we define, in this paper, an invariant Hex $_{n} (X)$ using the Hausdorff dimensions of the singular sets of $σ$ ’s and study its properties to deduce informations on the complex structure of $X$ .

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.

Holomorphic Cartan geometries and rational curves

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.

On the existence of bounded holomorphic functions on complete Kähler manifolds.

John S. Bland (1985)

Inventiones mathematicae

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Compact holomorphically pseudosymmetric Kähler manifolds

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.

Geometry of Kähler metrics and foliations by holomorphic discs

X. X. Chen, G. Tian (2008)

Publications Mathématiques de l'IHÉS

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On Holomorphic and Anti-Holomorphic Sectional Curvature of Indefinite Kähler Manifolds of Real Dimension n... 6.

Demir N. Kupeli (1993)

Manuscripta mathematica

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