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On natural metrics on tangent bundles of Riemannian manifolds

Mohamed Tahar Kadaoui Abbassi; Maâti Sarih — 2005

Archivum Mathematicum

There is a class of metrics on the tangent bundle $T M$ of a Riemannian manifold $(M, g)$ (oriented , or non-oriented, respectively), which are ’naturally constructed’ from the base metric $g$ [Kow-Sek1]. We call them “ $g$ -natural metrics" on $T M$ . To our knowledge, the geometric properties of these general metrics have not been studied yet. In this paper, generalizing a process of Musso-Tricerri (cf. [Mus-Tri]) of finding Riemannian metrics on $T M$ from some quadratic forms on $O M \times ℝ^{m}$ to find metrics (not necessary Riemannian)...

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