Publications de l'Institut Mathématique, Nouvelle Série Vol. 89(103), pp. 57–68 (2011) 

THE SCALAR CURVATURE OF THE TANGENT BUNDLE OF A FINSLER MANIFOLDAurel Bejancu and Hani Reda FarranDepartment of Mathematics and Computer Science, Kuwait University, Kuwait and Institute of Mathematics, Iasi Branch of the Romanian Academy, Romania; and Department of Mathematics and Computer Science, Kuwait University, KuwaitAbstract: 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. Keywords: Berwald manifold, Finsler manifold, Landsberg manifold, Riemannian manifold, scalar curvature, tangent bundle Classification (MSC2000): 53C60; 53C15 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 6 Apr 2011. This page was last modified: 16 Oct 2012.
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