Minimal Lagrangian connections on compact surfaces
arXiv:1609.08033 · doi:10.1016/j.aim.2019.106747
Abstract
We introduce the notion of a minimal Lagrangian connection on the tangent bundle of a manifold and classify all such connections in the case where the manifold is a compact oriented surface of non-vanishing Euler characteristic. Combining our classification with results of Labourie and Loftin, we conclude that every properly convex projective surface arises from a unique minimal Lagrangian connection.
32 pages
References in corpus (7)
- G2 geometry and integrable systems
- Survey on Affine Spheres
- Convex projective surfaces with compatible Weyl connection are hyperbolic
- Gauge theory on projective surfaces and anti-self-dual Einstein metrics in dimension four
- Holomorphic differentials, thermostats and Anosov flows
- Extremal conformal structures on projective surfaces
- Geometric Theory of Weyl Structures