Article
2022
·
7 citations
Vertical rescaled Cheeger-Gromoll metric and harmonicity on the cotangent bundle
Abstract
In this paper, we introduce the harmonicity on the cotangent bundle equipped with vertical rescaled Cheeger-Gromoll metric which rescales the vertical part by a non-zero differentiable function f. We establish a necessary and sufficient condition under which a covector field is harmonic with respect to this metric. We also construct some examples of harmonic vector fields. Finally, we study the harmonicity of a map between a Riemannian manifold and a cotangent bundle of another Riemannian manifold and vice versa.
Keywords
cotangent bundles
horizontal lift and vertical lift
vertical rescaled Cheeger-Gromoll metric
harmonic maps
WoS Categories
Mathematics
Citation
- Journal
- ADVANCED STUDIES-EURO-TBILISI MATHEMATICAL JOURNAL
- Year
- 2022
- Volume
- 15
- Issue
- 3
- Pages
- 11-29
- eISSN
- 2667-9930
- DOI
- 10.32513/asetmj/19322008221
- WoS UID
- WOS:000869744800002