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A classification of locally homogeneous affine connections on compact surfaces

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Abstract

We classify the affine connections on compact orientable surfaces for which the pseudogroup of local isometries acts transitively. We prove that such a connection is either torsion-free and flat, the Levi–Civita connection of a Riemannian metric of constant curvature or the quotient of a translation-invariant connection in the plane. This refines previous results by Opozda.

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Acknowledgments

We heartily thank Sorin Dumitrescu for many interesting conversations and for his comments on this text.

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Authors and Affiliations

  1. Unidad Cuernavaca, Instituto de Matemáticas, Universidad Nacional Autónoma de México, Av. Universidad s/n, Lomas de Chamilpa, 62210 , Cuernavaca, Morelos, Mexico

    Adolfo Guillot & Antonia Sánchez Godinez

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  1. Adolfo Guillot
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  2. Antonia Sánchez Godinez
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Correspondence to Adolfo Guillot.

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Partially supported by PAPIT-UNAM IN108214 (Mexico).

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Guillot, A., Sánchez Godinez, A. A classification of locally homogeneous affine connections on compact surfaces. Ann Glob Anal Geom 46, 335–349 (2014). https://doi.org/10.1007/s10455-014-9426-0

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  • DOI: https://doi.org/10.1007/s10455-014-9426-0

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