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Exotic spheres with lots of positive curvatures

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References

  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).

    Article  Google Scholar 

  2. Bazaikin, Y. On one family of 13-dimensional closed Riemannian positively curved manifolds,Sib. Math. J.,37, 1219–1237, (1996).

    Article  MathSciNet  Google Scholar 

  3. Berger, M. Les variétés riemanniennes homogènes normales simplemente connexes à courbure strictement positive,Ann. del Scoula Norm. Sup. Pisa,15, 179–246, (1961).

    MATH  Google Scholar 

  4. Cheeger, J. Some examples of manifolds of nonnegative curvature,J. Differential Geometry,8, 623–628, (1972).

    MathSciNet  Google Scholar 

  5. Davis, M. Some group actions on homotopy spheres of dimensions seven and fifteen,Am. J. of Math.,104, 59–90, (1982).

    Article  MATH  Google Scholar 

  6. Eells, J. and Kuiper, N. An invariant for certain smooth manifolds,Ann. di Mat. pura ed appl.,60, 93–110, (1963).

    Article  MathSciNet  Google Scholar 

  7. Eschenburg, J.-H. New examples of manifolds with strictly positive curvature,Invent. Math.,66, 469–480, (1982).

    Article  MathSciNet  MATH  Google Scholar 

  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. Fukaya, K. and Yamaguchi, T. The fundamental groups of almost nonnegatively curved manifolds,Ann. of Math.,136, 253–333, (1992).

    Article  MathSciNet  Google Scholar 

  10. Gluck, H., Warner, F., and Ziller, W. The geometry of the Hopf fibrations,L’Enseignement Mathémathique,32, 173–198, (1986).

    MathSciNet  MATH  Google Scholar 

  11. Gromoll, D. and Meyer, W. An exotic sphere with nonnegative sectional curvature,Ann. of Math.,100, 401–406, (1974).

    Article  MathSciNet  Google Scholar 

  12. Hatcher, A. A proof of the Smale Conjecture,Diff (S 3) ≃O(4),Ann. of Math.,117, 553–607, (1983).

    Article  MathSciNet  Google Scholar 

  13. Milnor, J. On manifolds homeomorphic to the 7-sphere,Annals of Math.,64, 399–405, (1956).

    Article  MathSciNet  Google Scholar 

  14. Nash, J. Positive Ricci curvature on fibre bundles,J. Diff. Geom.,14, 241–254, (1979).

    MathSciNet  MATH  Google Scholar 

  15. O’Neill, B. The fundamental equations of a submersion,Michigan Math. J.,13, 459–469, (1966).

    Article  MathSciNet  MATH  Google Scholar 

  16. Poor, W. Some exotic spheres with positive Ricci curvature,Math. Ann.,216, 245–252, (1975).

    Article  MathSciNet  MATH  Google Scholar 

  17. Rigas, A. Some bundles of non-negative curvature,Math. Ann.,232, 187–193, (1978).

    Article  MathSciNet  MATH  Google Scholar 

  18. Steenrod, N.Topology of Fiber Bundles, Princeton Mathematical Series, Princeton University Press, 1951.

  19. Wallach, N. Compact homogeneous Riemannian manifolds with strictly positive curvature,Ann. of Math.,96, 277–295,(1972).

    Article  MathSciNet  Google Scholar 

  20. Weinstein, A. Fat Bundles and symplectic manifolds,Advances in Mathematics,37, 239–250, (1980).

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Frederick Wilhelm.

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Wilhelm, F. Exotic spheres with lots of positive curvatures. J Geom Anal 11, 161–186 (2001). https://doi.org/10.1007/BF02921960

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