Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1995-1283536-1
MathSciNet review: 1283536
Full-text PDF

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 (17:298b)
  • [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), 231-241. MR 540942 (80h:53041)
  • [4] S. Kobayashi and K. Nomizu, Foundations of differential geometry. I, II, Wiley, New York, 1963, 1969.
  • [5] H. Matsushima and K. Okamoto, Non-existence of torsion free flat connections on a real semisimple Lie group, Hiroshima Math. J. 9 (1979), 59-60. MR 529327 (80f:53026)
  • [6] J. W. Milnor and J. D. Stasheff, Characteristic classes, Ann. of Math. Stud., no. 76, Princeton Univ. Press, Princeton, NJ, 1974. MR 0440554 (55:13428)

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: https://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

American Mathematical Society