Geodesic
Natural tensor fields of type $(0,2)$ on the tangent and cotangent bundles of a semi-Riemannian manifold
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 39 (2000) no. 1, p. 16

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Classification : 53C20, 53C50, 58A32 
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Araujo, José; Keilhauer, Guillermo. Natural tensor fields of type $(0,2)$ on the tangent and cotangent bundles of a semi-Riemannian manifold. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 39 (2000) no. 1, p. 16. http://geodesic.mathdoc.fr/item/AUPO_2000__39_1_a0/