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On connections, geodesics and sprays in synthetic differential geometry

Marta Bunge, Patrice Sawyer (1984)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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)...

Displaying 1 – 9 of 9

On connections, geodesics and sprays in synthetic differential geometry

On natural metrics on tangent bundles of Riemannian manifolds

On the creation of conjugate points.

On the discrete Godbillon-Vey invariant and Dehn surgery on geodesic flows

On the Entropy of the Geodesic Flow in Manifolds Without Conjugate Points.

On the Ergodicity of Frame Flows.

On the existence of escaping geodesics.

On the geodesics flow of tori without conjugate points.

On the Lengths of Closed Geodesics on Almost Round Spheres.

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