Geodesic
Invariant Einstein Metrics on Some Homogeneous Spaces of Classical Lie Groups
Canadian journal of mathematics, Tome 61 (2009) no. 6, pp. 1201-1213

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DOI

A Riemannian manifold $\left( M,\,\rho\right)$ is called Einstein if the metric $\rho $ satisfies the condition $\text{Ric}\left( \rho\right)\,=\,c\,\cdot \,\rho $ 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 $SO\left( n \right)/SO\left( l \right)$ . Furthermore, we show that for any positive integer $p$ there exists a Stiefel manifold $SO\left( n \right)/SO\left( l \right)$ that admits at least $p$ $SO\left( n \right)$ -invariant Einstein metrics.
DOI : 10.4153/CJM-2009-056-2
Mots-clés : 53C25, 53C30, Riemannian manifolds, homogeneous spaces, Einstein metrics, Stiefel manifolds 
Arvanitoyeorgos, Andreas; Dzhepko, V. V.; Nikonorov, Yu. G. Invariant Einstein Metrics on Some Homogeneous Spaces of Classical Lie Groups. Canadian journal of mathematics, Tome 61 (2009) no. 6, pp. 1201-1213. doi: 10.4153/CJM-2009-056-2
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     title = {Invariant {Einstein} {Metrics} on {Some} {Homogeneous} {Spaces} of {Classical} {Lie} {Groups}},
     journal = {Canadian journal of mathematics},
     pages = {1201--1213},
     year = {2009},
     volume = {61},
     number = {6},
     doi = {10.4153/CJM-2009-056-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2009-056-2/}
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