Minimal Lie group homomorphisms

A. Caminha

paper

Minimal Lie group homomorphisms

arXiv:0908.1259

Abstract

Let $G_{1}$ and $G_{2}$ be Lie groups furnished with bi-invariant metrics and $f : G_{1} \to G_{2}$ be a Lie group homomorphism which is also a minimal isometric immersion. If $G_{1}$ is compact and connected, we prove that either $G_{1}$ is isometric to a flat torus or $f$ is unstable as a harmonic map. We also apply this result to the case in which $f$ is the inclusion of a compact, connected Lie subgroup of a Lie group, as well as to construct several examples of unstable harmonic maps into the orthogonal group.

This paper has been withdraw due to a crucial sign error in the proof of the theorem