Article
2023
·
1 citations
ON THE COTANGENT BUNDLE AND UNIT COTANGENT BUNDLE WITH A GENERALIZED CHEEGER-GROMOLL METRIC
Abstract
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 differentiable function. Firstly, we investigate the curvature properties on the cotangent bundle with the generalized CheegerGromoll 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.
Keywords
Horizontal lift and vertical lift
cotangent bundles
generalized Cheeger-Gromoll metric
curvature tensor
WoS Categories
Mathematics
Citation
- Journal
- FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS
- Year
- 2023
- Volume
- 38
- Issue
- 1
- Pages
- 153-178
- ISSN
- 0352-9665
- eISSN
- 2406-047X
- DOI
- 10.22190/FUMI221101011Z
- WoS UID
- WOS:001043370600011