Geodesics on the Cotangent Bundle with Vertical Rescaled Cheeger-Gromoll Metric

Abstract

In this paper, we introduce the vertical rescaled Cheeger-Gromoll metric (deformation in the vertical bundle) on the cotangent bundle T*M over a Riemannian manifold (M, g) and we investigate the Levi-Civita connection of this metric. We study the geodesics on the cotangent bundle with respect to the vertical rescaled Cheeger-Gromoll metric. Afterward, we establish the necessary and sufficient conditions under which a curve be geodesic respect to this metric. Finally, we also construct some examples of geodesics.

Keywords

• cotangent bundles
• vertical rescaled Cheeger-Gromoll metric
• geodesics

References

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