ON THE COTANGENT BUNDLE AND UNIT COTANGENT BUNDLE WITH A GENERALIZED CHEEGER-GROMOLL METRIC

Facta Universitatis. Series Mathematics and Informatics

article

Abderrahim Zagane¹  Nour Elhouda Djaa¹  Aydin Gezer² 

[1] RELIZANE University;Ataturk University

关键词: Horizontal lift and vertical lift;    cotangent bundles;    generalized Cheeger-Gromoll metric;    curvature tensor.;   

DOI  :  10.22190/FUMI221101011Z

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Nishu / University of Nis

【 摘 要 】

In this paper, we consider a generalized Cheeger-Gromoll metric on a cotangent bundle over a Riemannian manifold, which is obtained by rescaling the vertical part of the Cheeger-Gromoll metric by a positive dierentiable function. Firstly, we investigate the curvature properties on the cotangent bundle with the generalized Cheeger-Gromoll metric. Secondly, we introduce the unit cotangent bundle equipped with this metric, where we present the formulas of the Levi-Civita connection and also all formulas of the Riemannian curvature tensors of this metric. Finally, we study the geodesics on the unit cotangent bundle with respect to this metric.

【 授权许可】

Unknown