Geodesic
On the geometry of frame bundles
Archivum mathematicum, Tome 48 (2012) no. 3, pp. 197-206.

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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.
DOI : 10.5817/AM2012-3-197
Classification : 53A30, 53C10, 53C24
Keywords: Riemannian manifold; frame bundle; tangent bundle; natural metric 
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Niedziałomski, Kamil. On the geometry of frame bundles. Archivum mathematicum, Tome 48 (2012) no. 3, pp. 197-206. doi : 10.5817/AM2012-3-197. http://geodesic.mathdoc.fr/articles/10.5817/AM2012-3-197/

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