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On curvature homogeneous and locally homogeneous affine connections

Author(s): Barbara Opozda
Journal: Proc. Amer. Math. Soc. 124 (1996), 1889-1893.
MSC (1991): Primary 53B05, 53C30
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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:

1.: S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, vol. I, Interscience Publishers, New York and London, 1963. MR 27:2945
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.
4.: B. Opozda and T. Sasaki, Surfaces whose images of the affine normal are curves, Kyushu J. Math. 49 (1995), 1--10.
5.: I. M. Singer, Infinitesimaly homogeneous spaces, Comm. Pure Appl. Math. 13 (1960), 685--697. MR 24:A1100

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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: 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
Copyright of article: Copyright 1996, American Mathematical Society


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