Invariant K�hler?Einstein metrics on compact homogeneous spaces

1986 ◽  
Vol 20 (3) ◽  
pp. 171-182 ◽  
Author(s):  
D. V. Alekseevskii ◽  
A. M. Perelomov
Keyword(s):  
Einstein Metrics ◽  
Homogeneous Spaces

scholarly journals Invariant Einstein Metrics on Some Homogeneous Spaces of Classical Lie Groups

2009 ◽  
Vol 61 (6) ◽  
pp. 1201-1213 ◽  
Author(s):  
Andreas Arvanitoyeorgos ◽  
V. V. Dzhepko ◽  
Yu. G. Nikonorov
Keyword(s):  
Riemannian Manifold ◽  
Positive Integer ◽  
Lie Groups ◽  
Einstein Metrics ◽  
Homogeneous Spaces ◽  
Classical Groups ◽  
Stiefel Manifolds ◽  
Additional Symmetries

Abstract A Riemannian manifold (M, ρ) is called Einstein if the metric ρ satisfies the condition Ric(ρ) = c · ρ for some constant c. This paper is devoted to the investigation of G-invariant Einstein metrics, with additional symmetries, on some homogeneous spaces G/H of classical groups. As a consequence, we obtain new invariant Einstein metrics on some Stiefel manifolds SO(n)/SO(l). Furthermore, we show that for any positive integer p there exists a Stiefelmanifold SO(n)/SO(l) that admits at least p SO(n)-invariant Einstein metrics.

Classification of invariant Einstein metrics on certain compact homogeneous spaces

2019 ◽  
Vol 63 (4) ◽  
pp. 755-776
Author(s):  
Zaili Yan ◽  
Huibin Chen ◽  
Shaoqiang Deng
Keyword(s):  
Einstein Metrics ◽  
Homogeneous Spaces

scholarly journals Kähler–Einstein Metrics on Smooth Fano Symmetric Varieties with Picard Number One

Mathematics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 102
Author(s):  
Jae-Hyouk Lee ◽  
Kyeong-Dong Park ◽  
Sungmin Yoo
Keyword(s):  
Einstein Metrics ◽  
Homogeneous Spaces ◽  
Picard Number ◽  
Spherical Varieties ◽  
Symmetric Varieties ◽  
Moment Polytope ◽  
Kähler Einstein Metrics ◽  
Moment Polytopes

Symmetric varieties are normal equivarient open embeddings of symmetric homogeneous spaces, and they are interesting examples of spherical varieties. We prove that all smooth Fano symmetric varieties with Picard number one admit Kähler–Einstein metrics by using a combinatorial criterion for K-stability of Fano spherical varieties obtained by Delcroix. For this purpose, we present their algebraic moment polytopes and compute the barycenter of each moment polytope with respect to the Duistermaat–Heckman measure.

scholarly journals Invariant Einstein Metrics on Certain Homogeneous Spaces

1997 ◽  
Vol 20 (1) ◽  
pp. 51-61 ◽  
Author(s):  
Joon-Sik PARK ◽  
Yusuke SAKANE
Keyword(s):  
Einstein Metrics ◽  
Homogeneous Spaces
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