Geodesic
Homogeneous Einstein metrics on Stiefel manifolds
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 3, pp. 627-634.

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A Stiefel manifold $V_k\bold R^n$ is the set of orthonormal $k$-frames in $\bold R^n$, and it is diffeomorphic to the homogeneous space $SO(n)/SO(n-k)$. We study $SO(n)$-invariant Einstein metrics on this space. We determine when the standard metric on $SO(n)/SO(n-k)$ is Einstein, and we give an explicit solution to the Einstein equation for the space $V_2\bold R^n$.
Classification : 53C20, 53C25, 53C30
Keywords: Riemannian geometry; homogeneous spaces; Einstein metrics; Stiefel manifolds 
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     author = {Arvanitoyeorgos, Andreas},
     title = {Homogeneous {Einstein} metrics on {Stiefel} manifolds},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {627--634},
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     number = {3},
     year = {1996},
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     zbl = {0881.53042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1996__37_3_a19/}
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Arvanitoyeorgos, Andreas. Homogeneous Einstein metrics on Stiefel manifolds. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 3, pp. 627-634. http://geodesic.mathdoc.fr/item/CMUC_1996__37_3_a19/