Great circle fibrations of the three-sphere
Herman Gluck and Frank W. Warner
Source: Duke Math. J. Volume 50, Number 1
(1983), 107-132.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077303001
Mathematical Reviews number (MathSciNet): MR700132
Zentralblatt MATH identifier: 0523.55020
Digital Object Identifier: doi:10.1215/S0012-7094-83-05003-2
References
[B] M. Berger, “Blaschke's Conjecture for Spheres” Appendix D in A. L. Besse, Manifolds All of Whose Geodesics are Closed, Springer Verlag Ergebnisse Series, vol. 93, Springer Verlag, 1978, pp. 236–242.
[G] H. Gluck, Dynamical behavior of geodesic fields, Global theory of dynamical systems (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1979), Lecture Notes in Math., vol. 819, Springer, Berlin, 1980, pp. 190–215.
Mathematical Reviews (MathSciNet): MR82c:58052
Zentralblatt MATH: 0448.58016
[G-W-Y] H. Gluck, F. W. 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, to appear.
[Ga] M. E. Gage, A note on skew-Hopf fibrations, to appear.
Mathematical Reviews (MathSciNet): MR766545
Zentralblatt MATH: 0527.55025
Digital Object Identifier: doi:10.2307/2044571
JSTOR: links.jstor.org
[Gr] L. W. Green, Auf Wiedersehensflächen, Ann. of Math. (2) 78 (1963), 289–299.
Mathematical Reviews (MathSciNet): MR27:5206
Digital Object Identifier: doi:10.2307/1970344
JSTOR: links.jstor.org
[H] H. Hopf, Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche, Math. Ann. 104 (1931), 637–665.
Zentralblatt MATH: 0001.40703
[K_1] J. L. Kazdan, “An Inequality Arising in Geometry” Appendix E in A. L. Besse, Manifolds All of Whose Geodesics are Closed, Springer Verlag Ergebnisse Series, vol. 93, Springer Verlag, 1978, pp. 243–246.
Mathematical Reviews (MathSciNet): MR496885
Zentralblatt MATH: 0387.53010
[K_2] J. L. Kazdan, An isoperimetric inequality and Wiedersehen manifolds, Seminar on Differential Geometry, Ann. of Math. Stud., vol. 102, Princeton Univ. Press, Princeton, N.J., 1982, pp. 143–157.
Mathematical Reviews (MathSciNet): MR83h:53059a
Zentralblatt MATH: 0491.53038
[M] J. Milnor, On manifolds homeomorphic to the $7$-sphere, Ann. of Math. (2) 64 (1956), 399–405.
Mathematical Reviews (MathSciNet): MR18,498d
Zentralblatt MATH: 0072.18402
Digital Object Identifier: doi:10.2307/1969983
JSTOR: links.jstor.org
[S] N. Steenrod, The Topology of Fibre Bundles, Princeton Mathematical Series, vol. 14, Princeton University Press, Princeton, N. J., 1951.
Mathematical Reviews (MathSciNet): MR12,522b
Zentralblatt MATH: 0054.07103
[W] A. Weinstein, On the volume of manifolds all of whose geodesics are closed, J. Differential Geometry 9 (1974), 513–517.
Mathematical Reviews (MathSciNet): MR52:11791
Zentralblatt MATH: 0289.53032
Project Euclid: euclid.jdg/1214432547
[Y_1] C. T. Yang, Odd-dimensional wiedersehen manifolds are spheres, J. Differential Geom. 15 (1980), no. 1, 91–96 (1981).
Mathematical Reviews (MathSciNet): MR82g:53049
Zentralblatt MATH: 0491.53039
Project Euclid: euclid.jdg/1214435386
[Y_2] C. T. Yang, On the Blaschke conjecture, Seminar on Differential Geometry, Ann. of Math. Stud., vol. 102, Princeton Univ. Press, Princeton, N.J., 1982, pp. 159–171.
Mathematical Reviews (MathSciNet): MR83h:53059b
Zentralblatt MATH: 0487.53041
[Y_3] C. T. Yang, Division algebras and fibrations of spheres by great spheres, J. Differential Geom. 16 (1981), no. 4, 577–593 (1982).
Mathematical Reviews (MathSciNet): MR83j:55013
Zentralblatt MATH: 0511.550160
Project Euclid: euclid.jdg/1214436369
[Y_4] C. T. Yang, Any Blaschke manifold of the homotopy type of $CP^n$ has the right volume, to appear.
Duke Mathematical Journal
