Some properties of Sasaki metric on tangent bundle of Finsler manifold

Document Type : Original Article


Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran.


Let (M,F) be a Finsler manifold and G be the Sasaki-Finsler metric on TM. In this paper, we investigate some properties of Sasaki-Finsler metric which is pure with respect to some paracomplex structures on TM. Also, we show that the curvature tensor field of the Levi-Civita connection on (TM,G) is recurrent or pseudo symmetric if and only if (M,F) is locally Eulidean or locally Minkowski space.