Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)

  • 1. Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol I, Interscience Publishers, a division of John Wiley & Sons, New York-London, 1963. MR 0152974 (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, Infinitesimally homogeneous spaces, Comm. Pure Appl. Math. 13 (1960), 685–697. MR 0131248 (24 #A1100)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 53B05, 53C30

Retrieve articles in all journals with MSC (1991): 53B05, 53C30

Additional Information

Barbara Opozda
Affiliation: Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059, Kraków, Poland

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

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia