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Locally homogeneous affine connections on compact surfaces


Author: Barbara Opozda
Journal: Proc. Amer. Math. Soc. 132 (2004), 2713-2721
MSC (2000): Primary 53C05, 53C40
DOI: https://doi.org/10.1090/S0002-9939-04-07402-7
Published electronically: April 9, 2004
MathSciNet review: 2054798
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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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Additional Information

Barbara Opozda
Affiliation: Instytut Matematyki Uniwersytet Jagielloński, ul. Reymonta 4, 30-059 Kraków, Poland
Email: opozda@im.uj.edu.pl

DOI: https://doi.org/10.1090/S0002-9939-04-07402-7
Keywords: Affine connection, local homogeneity
Received by editor(s): March 3, 2003
Received by editor(s) in revised form: June 16, 2003
Published electronically: April 9, 2004
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2004 American Mathematical Society

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