Quasihomogeneous analytic affine connections on surfaces

Abstract

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 quasihomogeneous, 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.

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Cited by in corpus (3)

• Gauge theory on projective surfaces and anti-self-dual Einstein metrics in dimension four
• A classification of locally homogeneous affine connections on compact surfaces
• Quasihomogeneous three-dimensional real analytic Lorentz metrics do not exist