On the geometry of the tangent bundle with vertical rescaled generalized Cheeger- Gromoll metric

Authors

  • L. Belarbi University of Mostaganem, Algeria
  • H. El hendi University of Bechar, Algeria
  • F. Letti University of Saida, Saida, Algeria

DOI:

https://doi.org/10.31926/but.mif.2019.12.61.2.5

Keywords:

horizontal lift, vertical lift, Cheeger-Gromoll metric, tangent bundle, harmonic map

Abstract

Let (M, g) be an n-dimensional smooth Riemannian manifold. In the present paper, we introduce a new class of natural metrics denoted by G f and called the vertical rescaled generalized Cheeger-Gromoll metric on the tangent bundle TM. We calculate its Levi-Civita connection and Riemannian curvature tensor. We study the geometry of (TM, G f).

Author Biographies

L. Belarbi, University of Mostaganem, Algeria

Department of Mathematics, Laboratory of Pure and Applied Mathematics,  (U.M.A.B.), B.P.227,27000

H. El hendi, University of Bechar, Algeria

Department of Mathematics, PO Box 417, 08000

F. Letti, University of Saida, Saida, Algeria

Department of Mathematics

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Published

2020-01-20

Issue

Vol. 12(61) No. 2 (2019)

Section

MATHEMATICS