The Curvature of the Hitchin Connection

TL;DR

This paper computes the curvature of the Hitchin connection and demonstrates that a slight modification can produce a curvature proportional to the Weil-Petersson form on Teichmüller space, linking geometric structures.

Contribution

It provides an explicit calculation of the Hitchin connection's curvature and relates a modified version to the Weil-Petersson symplectic form.

Findings

Curvature of the Hitchin connection is explicitly calculated.

A modified Hitchin connection has curvature proportional to the Weil-Petersson form.

Establishes a geometric link between Hitchin connection and Teichmüller space.

Abstract

In this paper we calculate the curvature of the Hitchin connection. We further show that a slight (possibly trivial) modification of the Hitchin connection has curvature equal to an explict given multiple of the Weil-Petersen symplectic form on Teichm\"{u}ller space.