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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On curvature homogeneous and locally
homogeneous affine connections


Author: Barbara Opozda
Journal: Proc. Amer. Math. Soc. 124 (1996), 1889-1893
MSC (1991): Primary 53B05, 53C30
MathSciNet review: 1342036
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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 [Enhancements On Off] (What's this?)

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  • 2. B. Opozda, Locally symmetric connections on surfaces, Results in Math. 20 (1991), 725--743. CMP 92:13
  • 3. ------, A class of projectively flat surfaces, Math. Z. 219 (1995), 77--92.
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03455-7
PII: S 0002-9939(96)03455-7
Keywords: Affine connections: locally homogenous, curvature homogeneous, projectively flat, locally symmetric
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
Article copyright: © Copyright 1996 American Mathematical Society