Quasihomogeneous analytic affine connections on surfaces

Sorin Dumitrescu (1) , Adolfo Guillot (2)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 UNAM - Instituto de Matematicas

We classify torsion-free real-analytic affine connections on compact oriented real-analytic surfaces which are locally homogeneous on a nontrivial open set, without being locally homogeneous on all of the surface. In particular, we prove that such connections exist. This classification relies in a local result that classifies germs of torsion-free real-analytic affine connections on a neighborhood of the origin in the plane which are quasiho- mogeneous, in the sense that they are locally homogeneous on an open set containing the origin in its closure, but not locally homogeneous in the neighborhood of the origin.

Mots clés: affine connections; normal forms

Domaines: Géométrie différentielle [math.DG]

Sorin Dumitrescu, Adolfo Guillot. Quasihomogeneous analytic affine connections on surfaces. Journal of Topology and Analysis, 2013, 5 (4), pp.491-532. ⟨10.1142/S1793525313500222⟩. ⟨hal-00816146⟩