Liouville Theorems for Dirac-Harmonic Maps

TL;DR

This paper establishes Liouville theorems for Dirac-harmonic maps from various geometric spaces to Riemannian manifolds, demonstrating conditions under which such maps must be trivial.

Contribution

It extends Liouville theorems to Dirac-harmonic maps from Euclidean, hyperbolic, and Schwarzschild spaces, broadening understanding of their rigidity properties.

Findings

Liouville theorems proven for Dirac-harmonic maps from Euclidean space

Liouville theorems proven for Dirac-harmonic maps from hyperbolic space

Liouville theorems proven for Dirac-harmonic maps from Schwarzschild space

Abstract

We prove Liouville theorems for Dirac-harmonic maps from the Euclidean space $\R^n$, the hyperbolic space $\H^n$ and a Riemannian manifold $\mathfrak{S^n}$ ($n\geq 3$) with the Schwarzschild metric to any Riemannian manifold $N$.