Minimal Surfaces in G2 Manifolds

TL;DR

This paper investigates conditions under which Riemann surface immersions into G2 manifolds are conformal and harmonic, using an associated Gauss map to establish criteria for minimal surfaces in these special geometries.

Contribution

It provides new criteria linking conformality, harmonicity, and the Gauss map for immersions into G2 manifolds, advancing understanding of minimal surfaces in exceptional holonomy spaces.

Findings

Criteria for conformal and harmonic immersions in G2 manifolds

Characterization of minimal surfaces via Gauss map

New insights into the geometry of G2 manifolds

Abstract

We consider immersions of a Riemann surface into a manifold with $G_2$-holonomy and give criteria for them to be conformal and harmonic, in terms of an associated Gauss map.