Skip to main content

A pinching problem for locally homogeneous spaces

Part of the Lecture Notes in Mathematics book series (LNM,volume 1201)

Keywords

  • Riemannian Manifold
  • Symmetric Space
  • Homogeneous Space
  • Ricci Curvature
  • Hausdorff Distance

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. W. Ambrose and I. M. Singer, On homogeneous Riemannian manifolds, Duke Math. J. 25 (1958) 647–669.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. M. Berger, Sur les variétés riemanniennes pincées juste audessous de 1/4, Ann. Inst. Fourier, 33 (1983) 135–150.

    CrossRef  MATH  Google Scholar 

  3. D. L. Brittain, A diameter pinching theorem for positive Ricci curvature, preprint.

    Google Scholar 

  4. C. B. Croke, An eigenvalue pinching theorem, Inv. Math. 68 (1982) 253–256.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. K. Fukaya, Theory of convergence for Riemannian orbifolds, preprint (1984).

    Google Scholar 

  6. R. E. Greene and H. Wu, Lipschitz convergence of Riemannian manifolds, preprint.

    Google Scholar 

  7. M. Gromov, Almost flat manifolds, J. Diff. Geom. 13 (1978) 231–241.

    MathSciNet  MATH  Google Scholar 

  8. —, Manifolds of negative curvature, J. Diff. Geom., 13 (1978), 223–230.

    MathSciNet  MATH  Google Scholar 

  9. —, Structures métriques pour les variétés riemanniennes, rédigé par J. Lafontaine et P. Pansu, Cedic/Fernand Nathan 1981.

    Google Scholar 

  10. A. Kasue, Applications of Laplacian and Hessian comparison theorems, Advanced Studies in Pure Math. 3, Geometry of Geodesics, 333–386.

    Google Scholar 

  11. A. Katsuda, Gromov's convergence theorems and its application, to appear in Nagoya Math. J. 100 (1985).

    Google Scholar 

  12. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, John Wilery, New York I 1963, II 1969.

    MATH  Google Scholar 

  13. Min-Oo and E. Ruh, Comparison theorems for compact symmetric spaces, Ann. Sci. Ecole Norm. Sup., 12 (1979) 335–353.

    MathSciNet  MATH  Google Scholar 

  14. —, Vanishing theorems and almost symmetric spaces of noncompact type, Math. Ann., 257 (1981), 419–433.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. D. Montgomery and L. Zippin, Topological transformation groups, Interscience, 1955.

    Google Scholar 

  16. E. Ruh, Almost flat manifolds, J. Diff. Geom., 17 (1982) 1–14.

    MathSciNet  MATH  Google Scholar 

  17. T. Sakai, Comparison and finiteness theorems in Riemannian geometry, Advanced Studies in Pure Math. 3, Geometry of Geodesics, 183–192.

    Google Scholar 

  18. F. Tricerri and L. Vanhecke, Homogeneous structures on Riemannian manifolds, London Math. Soc., Lect. Note Ser. 83, Cambridge Univ. Press 1983.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

Katsuda, A. (1986). A pinching problem for locally homogeneous spaces. In: Shiohama, K., Sakai, T., Sunada, T. (eds) Curvature and Topology of Riemannian Manifolds. Lecture Notes in Mathematics, vol 1201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075652

Download citation

  • DOI: https://doi.org/10.1007/BFb0075652

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16770-9

  • Online ISBN: 978-3-540-38827-2

  • eBook Packages: Springer Book Archive