Differential as a harmonic morphism with respect to Cheeger--Gromoll type metrics

TL;DR

This paper studies the conditions under which the differential of a map between Riemannian manifolds with Cheeger--Gromoll type metrics acts as a harmonic morphism, focusing on horizontal conformality and related properties.

Contribution

It provides a characterization of the differential as a harmonic morphism in the context of Cheeger--Gromoll type metrics on tangent bundles.

Findings

Characterization of harmonic morphisms with Cheeger--Gromoll metrics

Conditions for horizontal conformality of differentials

Insights into the geometry of tangent bundle maps

Abstract

We investigate horizontal conformality of a differential of a map between Riemannian manifolds where the tangent bundles are equipped with Cheeger--Gromoll type metrics. As a corollary, we characterize the differential of a map as a harmonic morphism.