scholarly journals Indefinite Kähler metrics of constant holomorphic sectional curvature

1990 ◽  
Vol 30 (3) ◽  
pp. 493-516
Author(s):  
Shigeyoshi Fujimura
Keyword(s):  
Sectional Curvature ◽  
Holomorphic Sectional Curvature ◽  
Kähler Metrics ◽  
Kahler Metrics

scholarly journals Complete Kähler–Einstein Metric on Stein Manifolds With Negative Curvature

2020 ◽  
Author(s):  
Man-Chun Lee
Keyword(s):  
Sectional Curvature ◽  
Ricci Flow ◽  
Negative Curvature ◽  
Einstein Metric ◽  
Holomorphic Sectional Curvature ◽  
Kähler Metrics ◽  
Stein Manifolds ◽  
Kahler Metrics ◽  
Negative Constant

Abstract We show the existence of complete negative Kähler–Einstein metric on Stein manifolds with holomorphic sectional curvature bounded from above by a negative constant. We prove that any Kähler metrics on such manifolds can be deformed to the complete negative Kähler–Einstein metric using the normalized Kähler–Ricci flow.

scholarly journals Geometry and topology of the space of Kähler metrics on singular varieties

2018 ◽  
Vol 154 (8) ◽  
pp. 1593-1632 ◽  
Author(s):  
Eleonora Di Nezza ◽  
Vincent Guedj
Keyword(s):  
Einstein Metrics ◽  
Normal Space ◽  
Fano Varieties ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Metric Properties ◽  
Singular Varieties ◽  
Underlying Space ◽  
And Topology ◽  
Kähler Einstein Metrics

Let $Y$ be a compact Kähler normal space and let $\unicode[STIX]{x1D6FC}\in H_{\mathit{BC}}^{1,1}(Y)$ be a Kähler class. We study metric properties of the space ${\mathcal{H}}_{\unicode[STIX]{x1D6FC}}$ of Kähler metrics in $\unicode[STIX]{x1D6FC}$ using Mabuchi geodesics. We extend several results of Calabi, Chen, and Darvas, previously established when the underlying space is smooth. As an application, we analytically characterize the existence of Kähler–Einstein metrics on $\mathbb{Q}$-Fano varieties, generalizing a result of Tian, and illustrate these concepts in the case of toric varieties.

scholarly journals Bianchi type A hyper-symplectic and hyper-Kähler metrics in 4D

2011 ◽  
Vol 29 (2) ◽  
pp. 025003 ◽  
Author(s):  
L C de Andrés ◽  
M Fernández ◽  
S Ivanov ◽  
J A Santisteban ◽  
L Ugarte ◽  
...  
Keyword(s):  
Bianchi Type ◽  
Type A ◽  
Kähler Metrics ◽  
Kahler Metrics
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