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Closed Geodesics on Riemannian Manifolds
Wilhelm Klingenberg
A co-publication of the AMS and CBMS.
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CBMS Regional Conference Series in Mathematics
1983; 79 pp; softcover
Number: 53
ISBN-10: 0-8218-0703-X
ISBN-13: 978-0-8218-0703-3
List Price: US$25
Member Price: US$20
All Individuals: US$20
Order Code: CBMS/53
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This book contains expository lectures from the CBMS Regional Conference held at the University of Florida, 1982.

The author considers a space formed by all closed curves in which the closed geodesics are characterized as the critical points of a functional, an idea going back to Morse. This exposition gives a refined version of Morse's approach which has several advantages over the old one--in particular, it possesses a canonical \(\mathbf O(2)\)-action.

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Table of Contents

  • The Hilbert manifold of \(H^1\)-curves
  • The loop space and the space of closed curves
  • The second order neighborhood of a critical point Appendix. The \(S^1\)- and the \(Z_2\)-action on \(\Lambda M\)
  • Closed geodesics on spheres
  • On the existence of infinitely many closed geodesics
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