scholarly journals Integrable systems and Special Kähler metrics

2021 ◽  
Vol 8 (1) ◽  
pp. 163-178
Author(s):  
Nigel Hitchin
Keyword(s):  
Integrable Systems ◽  
Kähler Metrics ◽  
Kahler Metrics

scholarly journals HYPER-KÄHLER METRICS BUILDING AND INTEGRABLE MODELS

1994 ◽  
Vol 09 (34) ◽  
pp. 3163-3173 ◽  
Author(s):  
E.H. SAIDI ◽  
M.B. SEDRA
Keyword(s):  
Integrable Systems ◽  
Constraint Equation ◽  
Integrable Models ◽  
Explicit Solutions ◽  
Harmonic Superspace ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Conserved Currents

Methods developed for the analysis of integrable systems are used to study the problem of hyper-Kähler metrics building as formulated in D=2, N=4 supersymmetric harmonic superspace. We show in particular that the constraint equation [Formula: see text] and its Toda-like generalizations are integrable. Explicit solutions together with the conserved currents generating the symmetry responsible for the integrability of these equations are given. Other features are also discussed.

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

scholarly journals Conics, twistors, and anti-self-dual tri-Kähler metrics

2020 ◽  
Vol 24 (4) ◽  
pp. 621-652
Author(s):  
Maciej Dunajski ◽  
Paul Tod
Keyword(s):  
Kähler Metrics ◽  
Kahler Metrics
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