Geodesic
The Existence Problem of Hyperbolic Structures on Vector Bundles
Publications de l'Institut Mathématique, _N_S_53 (1993) no. 67, p. 133

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Hyperbolic structures are defined on differentiable manifolds by Libermann [7] and then studied by many other authors. We extend these structures to arbitrary vector bundles and give necessary and sufficient conditions for the existance of such structures.
Classification : 53C15 
Cornelia-Livia Bejan. The Existence Problem of Hyperbolic Structures on Vector Bundles. Publications de l'Institut Mathématique, _N_S_53 (1993) no. 67, p. 133 . http://geodesic.mathdoc.fr/item/PIM_1993_N_S_53_67_a17/
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     title = {The {Existence} {Problem} of {Hyperbolic} {Structures} on {Vector} {Bundles}},
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