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On distinguished local coordinates for locally homogeneous affine surfaces

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Abstract

We give a new short self-contained proof of the result of Opozda (Differ Geom Appl 21:173–198, 2004) classifying the locally homogeneous torsion free affine surfaces and the extension to the case of surfaces with torsion due to Arias-Marco and Kowalski (Monatsh Math 153:1–18, 2008). Our approach rests on a direct analysis of the affine Killing equations and is quite different than the approaches taken previously in the literature.

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Authors and Affiliations

  1. Differential Geometry and its Applications Research Group, Escola Politécnica Superior, Universidade da Coruña, 15403, Ferrol, Spain

    M. Brozos-Vázquez

  2. Faculty of Mathematics, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    E. García-Río

  3. Mathematics Department, University of Oregon, Eugene, OR, 97403-1222, USA

    P. Gilkey

Authors
  1. M. Brozos-Vázquez
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  2. E. García-Río
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  3. P. Gilkey
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Corresponding author

Correspondence to E. García-Río.

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Communicated by Andreas Cap.

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Supported by projects MTM2016-75897-P and ED431C 2019/10 (European FEDER support included, UE).

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Brozos-Vázquez, M., García-Río, E. & Gilkey, P. On distinguished local coordinates for locally homogeneous affine surfaces. Monatsh Math 192, 65–74 (2020). https://doi.org/10.1007/s00605-020-01382-y

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  • DOI: https://doi.org/10.1007/s00605-020-01382-y

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