The scalar curvature of the tangent bundle of a Finsler manifold
Keyword(s):
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 ?~ 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 ?~ 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 ?~ satisfies the above condition.
2017 ◽
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2021 ◽
Vol 62
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