scholarly journals Distinguished Kähler metrics on Hirzebruch surfaces

1995 ◽  
Vol 347 (3) ◽  
pp. 1013-1021
Author(s):  
Andrew D. Hwang ◽  
Santiago R. Simanca
Keyword(s):  
Kähler Metrics ◽  
Kahler Metrics ◽  
Hirzebruch Surfaces

Distinguished Kahler Metrics on Hirzebruch Surfaces

1995 ◽  
Vol 347 (3) ◽  
pp. 1013 ◽  
Author(s):  
Andrew D. Hwang ◽  
Santiago R. Simanca
Keyword(s):  
Kähler Metrics ◽  
Kahler Metrics ◽  
Hirzebruch Surfaces

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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