Smooth great circle fibrations and an application to the topological Blaschke conjecture
HTML articles powered by AMS MathViewer
- by C. T. Yang PDF
- Trans. Amer. Math. Soc. 320 (1990), 507-524 Request permission
Abstract:
We study great smooth circle fibrations of round spheres and Blaschke manifolds of the homotopy type of complex projective spaces.References
- Arthur L. Besse, Manifolds all of whose geodesics are closed, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 93, Springer-Verlag, Berlin-New York, 1978. With appendices by D. B. A. Epstein, J.-P. Bourguignon, L. Bérard-Bergery, M. Berger and J. L. Kazdan. MR 496885
- W. Browder and G. R. Livesay, Fixed point free involutions on homotopy spheres, Bull. Amer. Math. Soc. 73 (1967), 242–245. MR 206965, DOI 10.1090/S0002-9904-1967-11700-2
- Herman Gluck, Frank Warner, and C. T. Yang, Division algebras, fibrations of spheres by great spheres and the topological determination of space by the gross behavior of its geodesics, Duke Math. J. 50 (1983), no. 4, 1041–1076. MR 726317, DOI 10.1215/S0012-7094-83-05044-5
- J. Milnor, Morse theory, Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, N.J., 1963. Based on lecture notes by M. Spivak and R. Wells. MR 0163331
- John W. Milnor and James D. Stasheff, Characteristic classes, Annals of Mathematics Studies, No. 76, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974. MR 0440554
- Deane Montgomery and C. T. Yang, Free differentiable actions on homotopy spheres, Proc. Conf. on Transformation Groups (New Orleans, La., 1967) Springer, New York, 1968, pp. 175–192. MR 0245042
- D. Montgomery and C. T. Yang, Differentiable transformation groups on homotopy spheres, Michigan Math. J. 14 (1967), 33–46. MR 217815
- Hajime Sato, On topological Blaschke conjecture. I. Cohomological complex projective spaces, Geometry of geodesics and related topics (Tokyo, 1982) Adv. Stud. Pure Math., vol. 3, North-Holland, Amsterdam, 1984, pp. 231–238. MR 758656, DOI 10.2969/aspm/00310231
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 320 (1990), 507-524
- MSC: Primary 55R25; Secondary 57R50
- DOI: https://doi.org/10.1090/S0002-9947-1990-1028766-9
- MathSciNet review: 1028766