Rocky Mountain Journal of Mathematics

Bounds on Characteristic Numbers by Curvature and Radius

Fernando Galaz-Garcia

Full-text: Open access

Article information

Source
Rocky Mountain J. Math. Volume 39, Number 4 (2009), 1225-1231.

Dates
First available in Project Euclid: 22 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1248269778

Digital Object Identifier
doi:10.1216/RMJ-2009-39-4-1225

Mathematical Reviews number (MathSciNet)
MR2524710

Zentralblatt MATH identifier
1175.53047

Subjects
Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Secondary: 57R20: Characteristic classes and numbers

Citation

Galaz-Garcia, Fernando. Bounds on Characteristic Numbers by Curvature and Radius. Rocky Mountain J. Math. 39 (2009), no. 4, 1225--1231. doi:10.1216/RMJ-2009-39-4-1225. https://projecteuclid.org/euclid.rmjm/1248269778


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References

  • M. Berger, On the characteristic of positively-pinched Riemannian manifolds, Proc. National Acad. Sci. 48 (1962), 1915-1917.
  • R.L. Bishop and S.I. Goldberg, On curvature and Euler-Poincaré characteristic, Proc. National Acad. Sci. 49 (1963), 814-817.
  • --------, Some implications of the generalized Gauss-Bonnet theorem, Trans. Amer. Math. Soc. 112 (1964), 508-535.
  • J.P. Bourguignon and H. Karcher, Curvature operators: Pinching estimates and geometric examples, Ann. Sci. École Norm. 11 (1978), 71-92.
  • A. Dessai and W. Tuschmann, Nonnegative curvature and cobordism type, Math. Z. 257 (2007), 7-12.
  • I.S. Gradshteyn and I.M. Ryshik, Tables of integrals, series, and products, 6th ed., Academic Press, San Diego, 2000%,.
  • W. Gröbner and N. Hofreiter, Integraltafel. Erster Teil. Unbestimmte Integrale., Springer-Verlag, Vienna, 1949.
  • M. Gromov, Curvature, diameter and Betti numbers, Comment. Math. Helv. 56 (1981), 179-195.
  • S. Kobayashi and K. Nomizu, Foundations of differential geometry, vol. II, Interscience Tracts Pure Appl. Math. 15, Interscience Publishers, John Wiley & Sons, Inc., 1969.
  • J. Milnor and J. Stasheff, Characteristic classes, Princeton University Press and University of Tokyo Press, 1974.
  • M. Spivak, A comprehensive introduction to differential geometry, second ed., vol. V, Publish or Perish, Wilmington, Delaware, 1979.
  • G. Tsagas, On the Pontrjagin numbers of positively-pinched Riemannian manifolds, Tensor (N.S.) 21 (1970), 377-379.