Minimal Lagrangian Connections on Compact Surfaces

Thomas Mettler

Institut für Mathematik, Goethe-Universität Frankfurt, Frankfurt am Main, Germany

Date: March 4, 2019

Published Version: Adv. Math. 354 (2019), Article ID 106747, 36 pp.

1.2 Minimal Lagrangian connections

1.3 Related work

2 Preliminaries

2.1 The coframe bundle

2.2 The orthonormal coframe bundle

2.3 The cotangent bundle and induced structures

3 Twisted Weyl connections

4 Submanifold theory of Lagrangian connections

4.1 Algebraic preliminaries

4.2 The mean curvature form

4.3 Minimality and the Liouville curvature

5 Minimal Lagrangian connections

6 The spherical case

7 The case of negative Euler-characteristic

7.1 Classification

7.2 Concluding remarks