Hyperbolic Kähler manifolds and proper holomorphic mappings to Riemann surfaces

2001 ◽  
Vol 11 (2) ◽  
pp. 382-406 ◽  
Author(s):  
T. Napier ◽  
M. Ramachandran
Keyword(s):  
Riemann Surfaces ◽  
Holomorphic Mappings ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Proper Holomorphic Mappings

scholarly journals Proper holomorphic mappings between hyperbolic product manifolds

2014 ◽  
Vol 25 (04) ◽  
pp. 1450039 ◽  
Author(s):  
Jaikrishnan Janardhanan
Keyword(s):  
Riemann Surfaces ◽  
Holomorphic Mappings ◽  
Complex Manifolds ◽  
Finiteness Theorem ◽  
Important Special Case ◽  
Full Result ◽  
Hyperbolic Riemann Surfaces ◽  
Special Case ◽  
Proper Holomorphic Mappings

We prove a result on the structure of finite proper holomorphic mappings between complex manifolds that are products of hyperbolic Riemann surfaces. While an important special case of our result follows from the ideas developed by Remmert and Stein, the proof of the full result relies on the interplay of the latter ideas and a finiteness theorem for Riemann surfaces.

Stability of pseudoconvexity of disc bundles over compact Riemann surfaces and application to a family of Galois coverings

2015 ◽  
Vol 26 (04) ◽  
pp. 1540003 ◽  
Author(s):  
Takeo Ohsawa
Keyword(s):  
Automorphism Group ◽  
Unit Disc ◽  
Riemann Surfaces ◽  
Kähler Manifolds ◽  
Transformation Groups ◽  
Kahler Manifolds ◽  
Discrete Subgroups ◽  
Stein Manifolds ◽  
Galois Coverings ◽  
Compact Riemann Surfaces

It is proved that Galois coverings of smooth families of compact Riemann surfaces over Stein manifolds are holomorphically convex if the covering transformation groups are isomorphic to discrete subgroups of the automorphism group of the unit disc. The proof is based on an extension of the fact that disc bundles over compact Kähler manifolds are weakly 1-complete.

Sunada transplantation and isogeny of intermediate Jacobians of compact Kähler manifolds

2020 ◽  
Vol 72 (1) ◽  
pp. 127-147
Author(s):  
Carolyn Gordon ◽  
Eran Makover ◽  
Bjoern Muetzel ◽  
David Webb
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds

Holomorphically projective mappings between generalized m-parabolic Kähler manifolds

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4865-4873 ◽  
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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