| Title:
|
Metrics with homogeneous geodesics on flag manifolds (English) |
| Author:
|
Alekseevsky, Dmitri |
| Author:
|
Arvanitoyeorgos, Andreas |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
2 |
| Year:
|
2002 |
| Pages:
|
189-199 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A geodesic of a homogeneous Riemannian manifold $(M=G/K, g)$ is called homogeneous if it is an orbit of an one-parameter subgroup of $G$. In the case when $M=G/H$ is a naturally reductive space, that is the $G$-invariant metric $g$ is defined by some non degenerate biinvariant symmetric bilinear form $B$, all geodesics of $M$ are homogeneous. We consider the case when $M=G/K$ is a flag manifold, i.e\. an adjoint orbit of a compact semisimple Lie group $G$, and we give a simple necessary condition that $M$ admits a non-naturally reductive invariant metric with homogeneous geodesics. Using this, we enumerate flag manifolds of a classical Lie group $G$ which may admit a non-naturally reductive $G$-invariant metric with homogeneous geodesics. (English) |
| Keyword:
|
homogeneous Riemannian spaces |
| Keyword:
|
homogeneous geodesics |
| Keyword:
|
flag manifolds |
| MSC:
|
03E25 |
| MSC:
|
14M15 |
| MSC:
|
53C22 |
| MSC:
|
53C30 |
| idZBL:
|
Zbl 1090.53044 |
| idMR:
|
MR1922121 |
| . |
| Date available:
|
2009-01-08T19:21:05Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119313 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
