On a borderline class of non-positively curved compact Kähler manifolds

Topology of positively curved compact Kähler manifolds had been studied by several authors (cf. [6; 2]); these manifolds are simply connected and their second Betti number is one [1]. We will restrict ourselves to the study of some compact homogeneous Kähler manifolds. The aim of this paper is to supplement some results in [9]. We prove, among other results, that a compact, simply connected homogeneous complex manifold whose Euler number is a prime p ≥ 2 is isomorphic to the complex projective space Pp-1 (C); in the p-1 case of surfaces, we prove that a compact, simply connected, homogeneous almost complex surface with Euler-Poincaré characteristic positive, is hermitian symmetric.

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Nevanlinna-type theorems for meromorphic functions on non-positively curved Kähler manifolds

Forum Mathematicum ◽

10.1515/forum-2016-0032 ◽

2018 ◽

Vol 30 (1) ◽

pp. 171-189

Author(s):

Atsushi Atsuji

Keyword(s):

Ricci Curvature ◽

Remainder Term ◽

Nevanlinna Theory ◽

Meromorphic Functions ◽

Kähler Manifolds ◽

Characteristic Functions ◽

Kahler Manifolds ◽

Second Main Theorem ◽

Positively Curved

Abstract We give a second main theorem of Nevanlinna theory on complete non-positively curved Kähler manifolds. Its remainder term depends only on Ricci curvature of the manifolds except for the terms depending only on the characteristic functions.

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Interpolation in non-positively curved Kähler manifolds

Journal of Geometric Analysis ◽

10.1007/bf02931003 ◽

2003 ◽

Vol 13 (1) ◽

pp. 173-183

Author(s):

Christophe Mourougane

Keyword(s):

Kähler Manifolds ◽

Kahler Manifolds ◽

Positively Curved

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Sunada transplantation and isogeny of intermediate Jacobians of compact Kähler manifolds

Tohoku Mathematical Journal ◽

10.2748/tmj/1585101624 ◽

2020 ◽

Vol 72 (1) ◽

pp. 127-147

Author(s):

Carolyn Gordon ◽

Eran Makover ◽

Bjoern Muetzel ◽

David Webb

Keyword(s):

Kähler Manifolds ◽

Kahler Manifolds

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Holomorphically projective mappings between generalized m-parabolic Kähler manifolds

Filomat ◽

10.2298/fil1715865p ◽

2017 ◽

Vol 31 (15) ◽

pp. 4865-4873 ◽

Cited By ~ 1

Author(s):

Milos Petrovic

Keyword(s):

Linear Systems ◽

Kähler Manifolds ◽

Kahler Manifolds ◽

Covariant Derivatives ◽

Linearly Independent ◽

Non Linear ◽

Non Linear Systems ◽

Curvature Tensors ◽

Derivatives Of

Generalized m-parabolic K?hler manifolds are defined and holomorphically projective mappings between such manifolds have been considered. Two non-linear systems of PDE?s in covariant derivatives of the first and second kind for the existence of such mappings are given. Also, relations between five linearly independent curvature tensors of generalized m-parabolic K?hler manifolds with respect to these mappings are examined.

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