| Title:
|
Invariance of $g$-natural metrics on linear frame bundles (English) |
| Author:
|
Kowalski, Oldřich |
| Author:
|
Sekizawa, Masami |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
44 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
139-147 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we prove that each $g$-natural metric on a linear frame bundle $LM$ over a Riemannian manifold $(M, g)$ is invariant with respect to a lifted map of a (local) isometry of the base manifold. Then we define $g$-natural metrics on the orthonormal frame bundle $OM$ and we prove the same invariance result as above for $OM$. Hence we see that, over a space $(M, g)$ of constant sectional curvature, the bundle $OM$ with an arbitrary $g$-natural metric $\tilde{G}$ is locally homogeneous. (English) |
| Keyword:
|
Riemannian manifold |
| Keyword:
|
linear frame bundle |
| Keyword:
|
orthonormal frame bundle |
| Keyword:
|
$g$-natural metrics |
| Keyword:
|
homogeneity |
| MSC:
|
53C07 |
| MSC:
|
53C20 |
| MSC:
|
53C21 |
| MSC:
|
53C40 |
| idZBL:
|
Zbl 1212.53042 |
| idMR:
|
MR2432851 |
| . |
| Date available:
|
2008-07-24T13:18:00Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116931 |
| . |
| 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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