The Journal of Geometric Analysis

, Volume 11, Issue 1, pp 161–186

Exotic spheres with lots of positive curvatures

Article

Math Subject Classifications

53C20 

Key Words and Phrases

curvature and exotic spheres 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Allof, S. and Wallach, N. An infinite family of distinct 7-manifolds admitting positively curved Riemannian structures,Bull. A.M.S.,81, 93–97, (1975).CrossRefGoogle Scholar
  2. [2]
    Bazaikin, Y. On one family of 13-dimensional closed Riemannian positively curved manifolds,Sib. Math. J.,37, 1219–1237, (1996).CrossRefMathSciNetGoogle Scholar
  3. [3]
    Berger, M. Les variétés riemanniennes homogènes normales simplemente connexes à courbure strictement positive,Ann. del Scoula Norm. Sup. Pisa,15, 179–246, (1961).MATHGoogle Scholar
  4. [4]
    Cheeger, J. Some examples of manifolds of nonnegative curvature,J. Differential Geometry,8, 623–628, (1972).MathSciNetGoogle Scholar
  5. [5]
    Davis, M. Some group actions on homotopy spheres of dimensions seven and fifteen,Am. J. of Math.,104, 59–90, (1982).CrossRefMATHGoogle Scholar
  6. [6]
    Eells, J. and Kuiper, N. An invariant for certain smooth manifolds,Ann. di Mat. pura ed appl.,60, 93–110, (1963).CrossRefMathSciNetGoogle Scholar
  7. [7]
    Eschenburg, J.-H. New examples of manifolds with strictly positive curvature,Invent. Math.,66, 469–480, (1982).CrossRefMathSciNetMATHGoogle Scholar
  8. [8]
    Eschenburg, J.-H. Freie isometrische Aktionen auf kompakten Liegruppen mit positiv gekrümmten Orbiträumen,Schriftenreihe Math. Inst. Univ. Münster, Ser. 2, vol. 32, Univ. Münster, Münster, 1984.Google Scholar
  9. [9]
    Fukaya, K. and Yamaguchi, T. The fundamental groups of almost nonnegatively curved manifolds,Ann. of Math.,136, 253–333, (1992).CrossRefMathSciNetGoogle Scholar
  10. [10]
    Gluck, H., Warner, F., and Ziller, W. The geometry of the Hopf fibrations,L’Enseignement Mathémathique,32, 173–198, (1986).MathSciNetMATHGoogle Scholar
  11. [11]
    Gromoll, D. and Meyer, W. An exotic sphere with nonnegative sectional curvature,Ann. of Math.,100, 401–406, (1974).CrossRefMathSciNetGoogle Scholar
  12. [12]
    Hatcher, A. A proof of the Smale Conjecture,Diff (S 3) ≃O(4),Ann. of Math.,117, 553–607, (1983).CrossRefMathSciNetGoogle Scholar
  13. [13]
    Milnor, J. On manifolds homeomorphic to the 7-sphere,Annals of Math.,64, 399–405, (1956).CrossRefMathSciNetGoogle Scholar
  14. [14]
    Nash, J. Positive Ricci curvature on fibre bundles,J. Diff. Geom.,14, 241–254, (1979).MathSciNetMATHGoogle Scholar
  15. [15]
    O’Neill, B. The fundamental equations of a submersion,Michigan Math. J.,13, 459–469, (1966).CrossRefMathSciNetMATHGoogle Scholar
  16. [16]
    Poor, W. Some exotic spheres with positive Ricci curvature,Math. Ann.,216, 245–252, (1975).CrossRefMathSciNetMATHGoogle Scholar
  17. [17]
    Rigas, A. Some bundles of non-negative curvature,Math. Ann.,232, 187–193, (1978).CrossRefMathSciNetMATHGoogle Scholar
  18. [18]
    Steenrod, N.Topology of Fiber Bundles, Princeton Mathematical Series, Princeton University Press, 1951.Google Scholar
  19. [19]
    Wallach, N. Compact homogeneous Riemannian manifolds with strictly positive curvature,Ann. of Math.,96, 277–295,(1972).CrossRefMathSciNetGoogle Scholar
  20. [20]
    Weinstein, A. Fat Bundles and symplectic manifolds,Advances in Mathematics,37, 239–250, (1980).CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Mathematica Josephina, Inc. 2001

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaRiverside

Personalised recommendations