Abstract
In this note we prove that on a simply-connected Stiefel manifold that is not a sphere, there are infinitely many closed geodesics in any riemannian metric.
This work was written under the support of SFB 170, "Geometrie und Analysis", at the Mathematisches Institut in Göttingen.
The typesetting of this paper was done using TECHNO-TYPE, which was designed by R.J. Milgram.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D. Gromoll and W. Meyer, Periodic geodesics on compact manifolds, J. Diff. Geom. 3(1969), 493–510.
P. Klein, Über die Kohomologie des freien Sleifenraumes, Bonner Math. Schriften 55(1972).
J. McCleary, User's Guide to Spectral Sequences, Publish or Perish Inc., to appear 1985.
J.C. Moore, Cartan's constructions, the homology of K(π, n)'s and some later developments, Astérique 32–33(1976), 173–212.
L. Smith, On the characteristic zero cohomology of the free loop space, Amer. J. Math. 103(1981), 887–910.
—, The Eilenberg-Moore spectral sequence and the mod 2 cohomology of certain fibre spaces, Ill. J. Math. 28(1984), 516–522.
A.S. Švarc, Homology of the space of closed curves, Trudy Moscov. Mat. Obsc. 9(1960), 3–44.
M. Vigué-Poirrier and D. Sullivan, The homology theory of the closed geodesic problem, J. Diff. Geom. 11(1976), 633–644.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1985 Springer-Verlag
About this paper
Cite this paper
McCleary, J. (1985). Closed geodesics on stiefel manifolds. In: Smith, L. (eds) Algebraic Topology Göttingen 1984. Lecture Notes in Mathematics, vol 1172. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074429
Download citation
DOI: https://doi.org/10.1007/BFb0074429
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16061-8
Online ISBN: 978-3-540-39745-8
eBook Packages: Springer Book Archive