| Title:
|
On the geometry of frame bundles (English) |
| Author:
|
Niedziałomski, Kamil |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
48 |
| Issue:
|
3 |
| Year:
|
2012 |
| Pages:
|
197-206 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $(M,g)$ be a Riemannian manifold, $L(M)$ its frame bundle. We construct new examples of Riemannian metrics, which are obtained from Riemannian metrics on the tangent bundle $TM$. We compute the Levi–Civita connection and curvatures of these metrics. (English) |
| Keyword:
|
Riemannian manifold |
| Keyword:
|
frame bundle |
| Keyword:
|
tangent bundle |
| Keyword:
|
natural metric |
| MSC:
|
53A30 |
| MSC:
|
53C10 |
| MSC:
|
53C24 |
| idMR:
|
MR2995872 |
| DOI:
|
10.5817/AM2012-3-197 |
| . |
| Date available:
|
2012-10-03T14:55:14Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142989 |
| . |
| Reference:
|
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| Reference:
|
[2] Baird, P., Wood, J. C.: Harmonic morphisms between Riemannian manifolds.Oxford University Press, Oxford, 2003. Zbl 1055.53049, MR 2044031 |
| Reference:
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[3] Benyounes, M., Loubeau, E., Wood, C. M.: Harmonic sections of Riemannian vector bundles, and metrics of Cheeger–Gromoll type.Differential Geom. Appl. 25 (3) (2007), 322–334. Zbl 1128.53037, MR 2330461, 10.1016/j.difgeo.2006.11.010 |
| 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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[9] Kowalski, O., Sekizawa, M.: On curvatures of linear frame bundles with naturally lifted metrics.Rend. Sem. Mat. Univ. Politec. Torino 63 (3) (2005), 283–295. Zbl 1141.53020, MR 2202049 |
| Reference:
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[10] Kowalski, O., Sekizawa, M.: On the geometry of orthonormal frame bundles.Math. Nachr. 281 (2008), no. 12, 1799–1809 281 (12) (2008), 1799–1809. Zbl 1158.53015, MR 2473330, 10.1002/mana.200610715 |
| Reference:
|
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| Reference:
|
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| . |
