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Kähler–Einstein metrics near an isolated log-canonical singularity
Journal für die Reine und Angewandte Mathematik, 2021We construct Kähler–Einstein metrics with negative scalar curvature near an isolated log canonical (non-log terminal) singularity. Such metrics are complete near the singularity if the underlying space has complex dimension 2.
V. Datar, Xin Fu, Jian Song
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G-uniform stability and Kähler–Einstein metrics on Fano varieties
Inventiones Mathematicae, 2019Let X be any $${{\mathbb {Q}}}$$ Q -Fano variety and $$\mathrm{Aut}(X)_0$$ Aut ( X ) 0 be the identity component of the automorphism group of X . Let $${\mathbb {G}}$$ G be a connected reductive subgroup of $$\mathrm{Aut}(X)_0$$ Aut ( X ) 0 that contains
Chi Li
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Kähler–Einstein metrics along the smooth continuity method
Geometric and Functional Analysis, 2016We show that if a Fano manifold M is K-stable with respect to special degenerations equivariant under a compact group of automorphisms, then M admits a Kähler–Einstein metric.
V. Datar, Gábor Székelyhidi
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Einstein Riemannian metrics and Einstein–Randers metrics on a class of homogeneous manifolds
Nonlinear Analysis: Theory, Methods & Applications, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kang, Yifang, Chen, Zhiqi
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Homogeneous Einstein metrics on Aloff-Wallach spaces
Differential Geometry and Its Applications, 1993 All homogeneous Einstein metrics on 7-dimensional Aloff-Wallach spaces Nk, l are described. For some of these spaces, the existence of homogeneous Einstein metrics with positive sectional curvature is ...
Kowalski, Oldřich +3 more
exaly +2 more sources
Letters in Mathematical Physics, 1999
The authors write an ansatz for quasi-Einstein Kähler metrics (also called Kähler Ricci solitons) and construct new examples on complex line bundles (or their compactifications \({\mathbf P}(\mathcal{O}\otimes L)\)) over Kähler-Einstein base manifolds \(B\). Firstly, the authors obtain in Sect. 2 an ansatz for quasi-Einstein Kähler metrics with a torus
Pedersen, Henrik +2 more
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The authors write an ansatz for quasi-Einstein Kähler metrics (also called Kähler Ricci solitons) and construct new examples on complex line bundles (or their compactifications \({\mathbf P}(\mathcal{O}\otimes L)\)) over Kähler-Einstein base manifolds \(B\). Firstly, the authors obtain in Sect. 2 an ansatz for quasi-Einstein Kähler metrics with a torus
Pedersen, Henrik +2 more
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K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics
Inventiones Mathematicae, 2015It is shown that any, possibly singular, Fano variety X admitting a Kähler-Einstein metric is K-polystable, thus confirming one direction of the Yau-Tian-Donaldson conjecture in the setting of $$\mathbb {Q}$$Q-Fano varieties equipped with their anti ...
R. Berman
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International Journal of Mathematics, 1995
Motivated by Koiso’s work on quasi-Einstein metrics on Fano manifolds, we define (generalized) quasi-Einstein metrics in any Kähler class on any compact complex manifold. It turns out that these metrics are similar to Calabi’s Extremal metrics. Moreover their existence might be studied by a curvature flow in a given Kähler class.
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Motivated by Koiso’s work on quasi-Einstein metrics on Fano manifolds, we define (generalized) quasi-Einstein metrics in any Kähler class on any compact complex manifold. It turns out that these metrics are similar to Calabi’s Extremal metrics. Moreover their existence might be studied by a curvature flow in a given Kähler class.
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On some euclidean einstein metrics
Letters in Mathematical Physics, 1986The authors study the complex manifold associated with a nonlinear superposition of the Eguchi-Hanson and the pseudo-Fubini-Study metrics. The apparent singularities of the metric can be resolved only if the Eguchi-Hanson parameter satisfies a certain condition with \(n\geq 3\). The authors give a geometrical explanation of this fact.
Pedersen, H., Nielsen, B.
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A comment on “A note on Einstein metrics”
ACM SIGSAM Bulletin, 1988In a recent note, Nielsen and Pedersen [1] reported how they verified some solutions of Einstein's field equations with the help of REDUCE. They used a program which is contained in the standard REDUCE [2] testfile and which was written by Barton and Fitch.
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