| Title:
|
Homogeneous Einstein metrics on Stiefel manifolds (English) |
| Author:
|
Arvanitoyeorgos, Andreas |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
627-634 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $V_2\bold R^n$. (English) |
| Keyword:
|
Riemannian geometry |
| Keyword:
|
homogeneous spaces |
| Keyword:
|
Einstein metrics |
| Keyword:
|
Stiefel manifolds |
| MSC:
|
53C20 |
| MSC:
|
53C25 |
| MSC:
|
53C30 |
| idZBL:
|
Zbl 0881.53042 |
| idMR:
|
MR1426927 |
| . |
| Date available:
|
2009-01-08T18:26:41Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118869 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/118895 |
| . |
| Reference:
|
[1] Besse A.L.: Einstein Manifolds.Springer-Verlag, Berlin, 1987. Zbl 1147.53001, MR 0867684 |
| Reference:
|
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| Reference:
|
[3] Cheeger J., Ebin D.G.: Comparison Theorems in Riemannian Geometry.North-Holland, Amsterdam, 1975. Zbl 1142.53003, MR 0458335 |
| Reference:
|
[4] James I.M.: The Topology of Stiefel Manifolds.Cambridge University Press, Lecture Note Series 24, Great Britain, 1976. Zbl 0337.55017, MR 0431239 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[9] Sagle A.A.: Some homogeneous Einstein manifolds.Nagoya Math. J. 39 (1970), 81-106. Zbl 0198.54801, MR 0271867 |
| Reference:
|
[10] Wang M.: Some examples of homogeneous Einstein manifolds in dimension seven.Duke Math. J. 49.1 (1982), 23-28. Zbl 0488.53035, MR 0650366 |
| Reference:
|
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| . |
