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).
Raei, Z. (2021). On the geometry of tangent bundle of Finsler manifold with Cheeger-Gromoll metric. Journal of Finsler Geometry and its Applications, 2(1), 1-30. doi: 10.22098/jfga.2021.1260
MLA
Zohre Raei. "On the geometry of tangent bundle of Finsler manifold with Cheeger-Gromoll metric". Journal of Finsler Geometry and its Applications, 2, 1, 2021, 1-30. doi: 10.22098/jfga.2021.1260
HARVARD
Raei, Z. (2021). 'On the geometry of tangent bundle of Finsler manifold with Cheeger-Gromoll metric', Journal of Finsler Geometry and its Applications, 2(1), pp. 1-30. doi: 10.22098/jfga.2021.1260
VANCOUVER
Raei, Z. On the geometry of tangent bundle of Finsler manifold with Cheeger-Gromoll metric. Journal of Finsler Geometry and its Applications, 2021; 2(1): 1-30. doi: 10.22098/jfga.2021.1260
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