scholarly journals Kähler manifolds with quasi-constant holomorphic curvature

2009 ◽  
Vol 36 (2) ◽  
pp. 143-159 ◽  
Author(s):  
Włodzimierz Jelonek
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Holomorphic Curvature

Isotropic and Kähler Immersions

1965 ◽  
Vol 17 ◽  
pp. 907-915 ◽  
Author(s):  
Barrett O'Neill
Keyword(s):  
Constant Curvature ◽  
Riemannian Manifolds ◽  
Isometric Immersion ◽  
Normal Curvature ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Real Constant ◽  
Cartesian Products ◽  
The Real ◽  
Holomorphic Curvature

Let Md and be Riemannian manifolds. We shall say that an isometric immersion ϕ: Md —> is isotropic provided that all its normal curvature vectors have the same length. The class of such immersions is closed under compositions and Cartesian products. Umbilic immersions (e.g. Sd ⊂ Rd+1) are isotropic, but the converse does not hold. If M and are Kähler manifolds of constant holomorphic curvature, then any Kähler immersion of M in is automatically isotropic (Lemma 6). We shall find the smallest co-dimension for which there exist non-trivial immersions of this type, and obtain similar results in the real constant-curvature case.

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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