Locally homogeneous affine connections on compact surfaces

Opozda, Barbara

doi:10.1090/S0002-9939-04-07402-7

Locally homogeneous affine connections on compact surfaces
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Proc. Amer. Math. Soc. 132 (2004), 2713-2721 Request permission

Abstract:

Global properties of locally homogeneous and curvature homogeneous affine connections are studied. It is proved that the only locally homogeneous connections on surfaces of genus different from 1 are metric connections of constant curvature. There exist nonmetrizable nonlocally symmetric locally homogeneous affine connections on the torus of genus 1. It is proved that there is no global affine immersion of the torus endowed with a nonflat locally homogeneous connection into ${\mathbf R} ^3$.

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