Locally homogeneous affine connections on compact surfaces
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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 ${\mathbf R} ^3$.References
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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
- 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
- © Copyright 2004 American Mathematical Society
- 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
- MathSciNet review: 2054798