Publications de l'Institut Mathematique 2011 Volume 89, Issue 103, Pages: 57-68
doi:10.2298/PIM1103057B
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The scalar curvature of the tangent bundle of a Finsler manifold

Bejancu Aurel, Farran Reda Hani

Let Fm = (M, F) be a Finsler manifold and G be the Sasaki-Finsler metric on the slit tangent bundle TM0 = TM \{0} of M. We express the scalar curvature ρ~ of the Riemannian manifold (TM0,G) in terms of some geometrical objects of the Finsler manifold Fm. Then, we find necessary and sufficient conditions for ρ~ to be a positively homogenenous function of degree zero with respect to the fiber coordinates of TM0. Finally, we obtain characterizations of Landsberg manifolds, Berwald manifolds and Riemannian manifolds whose ρ~ satisfies the above condition.

Keywords: Berwald manifold, Finsler manifold, Landsberg manifold, Riemannian manifold, scalar curvature, tangent bundle

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