Geodesic
The Scalar Curvature of the Tangent Bundle of a Finsler Manifold
Publications de l'Institut Mathématique, _N_S_89 (2011) no. 103, p. 57 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Let $\mathbb{F}^m=(M,F)$ be a Finsler manifold and $G$ be the Sasaki-Finsler metric on the slit tangent bundle $TM^0=TM\setminus\{0\}$ of $M$. We express the scalar curvature $\widetilde\rho$ of the Riemannian manifold $(TM^0,G)$ in terms of some geometrical objects of the Finsler manifold $\mathbb{F}^m$. Then, we find necessary and sufficient conditions for $\widetilde\rho$ to be a positively homogenenous function of degree zero with respect to the fiber coordinates of $TM^0$. Finally, we obtain characterizations of Landsberg manifolds, Berwald manifolds and Riemannian manifolds whose $\widetilde\rho$ satisfies the above condition.
Classification : 53C60 53C15
Keywords: Berwald manifold, Finsler manifold, Landsberg manifold, Riemannian manifold, scalar curvature, tangent bundle 
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     title = {The {Scalar} {Curvature} of the {Tangent} {Bundle} of a {Finsler} {Manifold}},
     journal = {Publications de l'Institut Math\'ematique},
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Aurel Bejancu; Hani Reda Farran. The Scalar Curvature of the Tangent Bundle of a Finsler Manifold. Publications de l'Institut Mathématique, _N_S_89 (2011) no. 103, p. 57 . http://geodesic.mathdoc.fr/item/PIM_2011_N_S_89_103_a5/