g-Natural metrics on unit tangent sphere bundles via a Musso-Tricerri process
E. Musso and F. Tricerri had given a process of construction of Riemannian metrics on tangent bundles and unit tangent bundles, over m-dimensional Riemannian manifolds (M, g), from some special quadratic forms an OM × R^m and OM, respectively, where OM is the bundle of orthonormal frames [7]. We pr...
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| Format: | Article |
| Language: | English |
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Sapienza Università Editrice
2010-01-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
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| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2010(3-4)/239-247.pdf |
| Summary: | E. Musso and F. Tricerri had given a process of construction of Riemannian metrics on tangent bundles and unit tangent bundles, over m-dimensional
Riemannian manifolds (M, g), from some special quadratic forms an OM × R^m and OM, respectively, where OM is the bundle of orthonormal frames [7]. We prove in this note that every Riemannian g-natural metric on the unit tangent sphere bundle over a Riemannian manifold can be constructed by the Musso-Tricerri’s process. As a corollary, we show that every Riemannian g-natural metric on the unit tangent bundle, over a two-point homogeneous space, is homogeneous. |
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| ISSN: | 1120-7183 2532-3350 |