The Ricci flow with metric torsion on closed surfaces

Abstract

The famous Uniformization Theorem states that on closed Riemannian surfaces there always exists a metric of constant curvature for the Levi-Cevita connection. In this article we prove that an analogue of the uniformization theorem also holds for connections with metric torsion in the case of non-positive Euler characteristic. Our main tool is an adapted form of the Ricci flow.

arXiv comment14 pages, published version

Cited by in corpus (2)

• Harmonic maps with torsion
• Affine Killing vector fields on homogeneous surfaces with torsion