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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On curvature homogeneous and locally homogeneous affine connections
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by Barbara Opozda PDF
Proc. Amer. Math. Soc. 124 (1996), 1889-1893 Request permission

Abstract:

This paper deals with curvature homogeneous affine connections on $2$-dimensional manifolds. We give a sufficient condition for a projectively flat curvature homogeneous connection to be locally homogeneous and show how to construct curvature homogeneous connections that are not locally homogeneous.
References
  • Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol I, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1963. MR 0152974
  • B. Opozda, Locally symmetric connections on surfaces, Results in Math. 20 (1991), 725–743.
  • —, A class of projectively flat surfaces, Math. Z. 219 (1995), 77–92.
  • B. Opozda and T. Sasaki, Surfaces whose images of the affine normal are curves, Kyushu J. Math. 49 (1995), 1–10.
  • I. M. Singer, Infinitesimally homogeneous spaces, Comm. Pure Appl. Math. 13 (1960), 685–697. MR 131248, DOI 10.1002/cpa.3160130408
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Additional Information
  • Barbara Opozda
  • Affiliation: Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059, Kraków, Poland
  • Email: opozda@im.uj.edu.pl
  • Received by editor(s): November 15, 1994
  • Additional Notes: The research was partially supported by the KBN grant no. 2 P301 030 04.
  • Communicated by: Christopher Croke
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 1889-1893
  • MSC (1991): Primary 53B05, 53C30
  • DOI: https://doi.org/10.1090/S0002-9939-96-03455-7
  • MathSciNet review: 1342036