On the Cheeger-Gromoll metric

TL;DR

This paper explores the properties of the Cheeger-Gromoll metric on tangent bundles, focusing on covariant derivatives, Killing vector fields, and curvature tensor components to deepen understanding of its geometric structure.

Contribution

It provides explicit calculations of the curvature tensor components of the Cheeger-Gromoll metric using adapted frames, advancing the geometric analysis of tangent bundles.

Findings

Explicit formulas for the curvature tensor components.

Characterization of Killing vector fields in the tangent bundle.

Insights into the geometric structure induced by the Cheeger-Gromoll metric.

Abstract

The purpose of this paper is to investigate applications the covariant derivatives, killing vector fields and to calculate the components of the curvature tensor CGR of the Cheeger-Gromoll metric with respect to adapted frames in a the Riemannian manifold to its tangent bundle T(Mn)