Some results on harmonic metrics

TL;DR

This paper establishes the equivalence of harmonicity between a metric on a pseudo-Riemannian manifold and its lifts to tangent and cotangent bundles, with applications discussed.

Contribution

It proves the harmonicity equivalence of a metric and its lifts on tangent and cotangent bundles, advancing understanding in differential geometry.

Findings

Harmonicity of a metric is equivalent to that of its lifts.

Includes applications of the harmonicity equivalence.

Provides new insights into harmonic metrics on bundles.

Abstract

In this paper, we prove that the harmonicity of a metric on a pseudo-Riemannian manifold is equivalent to the harmonicity of both its Sasaki (resp. horizontal and complete) lift metric on the tangent bundle and its Sasaki lift metric on the cotangent bundle. Some applications are included.