Two notes on harmonic distributions

TL;DR

This paper explores harmonic distributions on Riemannian manifolds, providing new examples and proving nonexistence results using tangent bundle lifts and conformal metric deformations.

Contribution

It introduces new examples of harmonic distributions and demonstrates their nonexistence on certain manifolds through novel geometric approaches.

Findings

New harmonic distributions found on some manifolds

Nonexistence results established for specific Riemannian manifolds

Two different methods used: tangent bundle lifting and conformal deformation

Abstract

We say that a distribution is harmonic if it is harmonic when considered as a section of a Grassmann bundle. We find new examples of harmonic distributions and show nonexistense of harmonic distrubutions on some Riemannian manifolds by two different approaches. Firstly, we lift distributions to the second tangent bundle equipped with the Sasaki metric. Secondly, we deform conformally the metric on a base manifold.