On the geometry of tangent bundle of Finsler manifold with Cheeger-Gromoll metric

Document Type : Original Article


Department of Mathematics, Faculty of Science, University of Mohaghegh Ardabili, Ardabil, Iran. Email: raei.zohre@gmail.com


Let (M, F) be a Finsler manifold and G be the Cheeger-Gromoll metric on TM induced
by F. We show that the curvature tensor field of the Levi-Civita connection on (TM,G) is
determined by the curvature tensor field of Vrãnceanu connection and some adapted tensor
fields on TM. Then we prove that (TM,G) is locally symmetric if and only if (M, F) is locally
Euclidean. Also, we express the flag curvature of the Finsler manifold (M, F).