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Closed geodesics on stiefel manifolds

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Book cover Algebraic Topology Göttingen 1984

Part of the book series: Lecture Notes in Mathematics ((2766,volume 1172))

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.

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References

  1. D. Gromoll and W. Meyer, Periodic geodesics on compact manifolds, J. Diff. Geom. 3(1969), 493–510.

    MathSciNet  MATH  Google Scholar 

  2. P. Klein, Über die Kohomologie des freien Sleifenraumes, Bonner Math. Schriften 55(1972).

    Google Scholar 

  3. J. McCleary, User's Guide to Spectral Sequences, Publish or Perish Inc., to appear 1985.

    Google Scholar 

  4. J.C. Moore, Cartan's constructions, the homology of K(π, n)'s and some later developments, Astérique 32–33(1976), 173–212.

    MATH  Google Scholar 

  5. L. Smith, On the characteristic zero cohomology of the free loop space, Amer. J. Math. 103(1981), 887–910.

    Article  MathSciNet  MATH  Google Scholar 

  6. —, The Eilenberg-Moore spectral sequence and the mod 2 cohomology of certain fibre spaces, Ill. J. Math. 28(1984), 516–522.

    MATH  Google Scholar 

  7. A.S. Švarc, Homology of the space of closed curves, Trudy Moscov. Mat. Obsc. 9(1960), 3–44.

    Google Scholar 

  8. M. Vigué-Poirrier and D. Sullivan, The homology theory of the closed geodesic problem, J. Diff. Geom. 11(1976), 633–644.

    MathSciNet  MATH  Google Scholar 

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Larry Smith

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© 1985 Springer-Verlag

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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

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  • DOI: https://doi.org/10.1007/BFb0074429

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16061-8

  • Online ISBN: 978-3-540-39745-8

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