Symmetric Spaces and Kähler Manifolds

2008 ◽  
pp. 243-299
Keyword(s):  
Symmetric Spaces ◽  
Kähler Manifolds ◽  
Kahler Manifolds

Coupled Vortex Equations on Complete Kähler Manifolds

2008 ◽  
Vol 51 (3) ◽  
pp. 467-480
Author(s):  
Yue Wang
Keyword(s):  
Symmetric Spaces ◽  
Existence Results ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Convex Domains ◽  
Hermitian Symmetric Spaces ◽  
Vortex Equations ◽  
Curved Manifolds ◽  
Pseudo Convex ◽  
Simply Connected

AbstractIn this paper, we first investigate the Dirichlet problem for coupled vortex equations. Secondly, we give existence results for solutions of the coupled vortex equations on a class of complete noncompact Kähler manifolds which include simply-connected strictly negative curved manifolds, Hermitian symmetric spaces of noncompact type and strictly pseudo-convex domains equipped with the Bergmann metric.

scholarly journals PARTIAL CLASSIFICATION RESULTS FOR POSITIVE QUATERNION KÄHLER MANIFOLDS

2012 ◽  
Vol 23 (02) ◽  
pp. 1250038
Author(s):  
MANUEL AMANN
Keyword(s):  
Scalar Curvature ◽  
Riemannian Manifolds ◽  
Symmetric Spaces ◽  
Positive Scalar Curvature ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
The Real ◽  
Positive Scalar ◽  
Partial Classification ◽  
Almost All

Positive Quaternion Kähler Manifolds are Riemannian manifolds with holonomy contained in Sp(n)Sp(1) and with positive scalar curvature. Conjecturally, they are symmetric spaces. We prove this conjecture in dimension 20 under additional assumptions and we provide recognition theorems for the real Grassmannian [Formula: see text] in almost all dimensions.

scholarly journals Real hypersurfaces with isometric Reeb flow in Kähler manifolds

2019 ◽  
Vol 23 (01) ◽  
pp. 1950039
Author(s):  
Jürgen Berndt ◽  
Young Jin Suh
Keyword(s):  
Symmetric Spaces ◽  
Kähler Manifolds ◽  
Real Hypersurfaces ◽  
Kahler Manifolds ◽  
Compact Type ◽  
Hermitian Symmetric Spaces

We investigate the structure of real hypersurfaces with isometric Reeb flow in Kähler manifolds. As an application we classify real hypersurfaces with isometric Reeb flow in irreducible Hermitian symmetric spaces of compact type.

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