Three-dimensional compact Heterotic solitons with parallel torsion

TL;DR

This paper classifies three-dimensional compact Heterotic solitons with parallel torsion, showing they are either hyperbolic manifolds or quotients of the Heisenberg group, and establishes a scalar curvature bound.

Contribution

It provides a rigidity classification for these solitons and introduces a universal scalar curvature bound, advancing understanding of their geometric structure.

Findings

Classified compact 3D Heterotic solitons with parallel torsion.

Identified solitons as hyperbolic manifolds or Heisenberg quotients.

Established a scalar curvature upper bound of -24.

Abstract

We obtain a rigidity result for compact three-dimensional Heterotic solitons with parallel non-trivial torsion. We show that they are either hyperbolic three-manifolds or compact quotients of the Heisenberg group equipped with a left-invariant metric. In particular, the latter arise both as solitons with completely skew-symmetric torsion as well as with non-vanishing twistorial component. As a corollary, we obtain the universal bound $-24$ for the scalar curvature of Heterotic solitons with parallel skew-symmetric torsion, which prevents it from being arbitrarily large.