Project «Minimal Lagrangian connections and related structures»

A projective structure on a smooth manifold consists of an equivalence class p of torsion-free connections on its tangent bundle, where two such connections are called equivalent if they have the same geodesics up to parametrisation.

The representative connections of a projective structure p on a smooth manifold M are in one-to-one correspondence with the sections of an affine bundle, whose total space carries a split-signature metric as well as a symplectic form, both of which are defined in a canonical fashion from p. Consequently, all the submanifold notions of (pseudo-)Riemannian geometry and symplectic geometry can be applied to the representative connections of p. This point of view gives rise to the notion of a minimal Lagrangian connection.

The aim of this research project is to investigate various questions related to minimal Lagrangian connections, in particular, to provide a characterisation of projective manifolds that arise from a minimal Lagrangian connection. 

Duration of project

01.01.2020 – 31.12.2022

Collaborators

Funding

  • SPP 2026 – Geometry at Infinity. Priority programm by Deutsche Forschungsgemeinschaft DFG

Links

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