Proceedings of the American Mathematical Society

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

 

 

An example of almost flat affine connections on the three-dimensional sphere


Author: Yoshio Agaoka
Journal: Proc. Amer. Math. Soc. 123 (1995), 3519-3521
MSC: Primary 53C05; Secondary 57R20
MathSciNet review: 1283536
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show the existence of almost flat affine structures on the three-dimensional sphere, and prove that the Pontryagin numbers serve as the obstruction to the existence of such structures.


References [Enhancements On Off] (What's this?)

  • [1] L. Auslander and L. Markus, Holonomy of flat affinely connected manifolds, Ann. of Math. (2) 62 (1955), 139–151. MR 0072518
  • [2] P. Buser and H. Karcher, Gromov's almost flat manifolds, Astérisque 81 (1981).
  • [3] M. Gromov, Almost flat manifolds, J. Differential Geom. 13 (1978), no. 2, 231–241. MR 540942
  • [4] S. Kobayashi and K. Nomizu, Foundations of differential geometry. I, II, Wiley, New York, 1963, 1969.
  • [5] Hiroshi Matsushima and Kiyosato Okamoto, Nonexistence of torsion free flat connections on a real semisimple Lie group, Hiroshima Math. J. 9 (1979), no. 1, 59–60. MR 529327
  • [6] John W. Milnor and James D. Stasheff, Characteristic classes, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974. Annals of Mathematics Studies, No. 76. MR 0440554

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C05, 57R20

Retrieve articles in all journals with MSC: 53C05, 57R20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1283536-1
Keywords: Affine connection, curvature, almost flat manifold, Pontryagin number
Article copyright: © Copyright 1995 American Mathematical Society