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Two classes of Riemannian manifolds whose geodesic flows are integrable


About this Title

Kazuyoshi Kiyohara

Publication: Memoirs of the American Mathematical Society
Publication Year 1997: Volume 130, Number 619
ISBNs: 978-0-8218-0640-1 (print); 978-1-4704-0208-2 (online)
DOI: http://dx.doi.org/10.1090/memo/0619
MathSciNet review: 1396959
MSC (1991): Primary 58F17; Secondary 53C22, 58F07

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Table of Contents


Chapters

  • Part 1. Liouville manifolds
  • Introduction
  • 1. Local structure of proper Liouville manifolds
  • 2. Global structure of proper Liouville manifolds
  • 3. Proper Liouville manifolds of rank one
  • Appendix. Simply connected manifolds of constant curvature
  • Part 2. Kähler-Liouville manifolds
  • Introduction
  • 1. Local calculus on
  • 2. Summing up the local data
  • 3. Structure of
  • 4. Torus action and the invariant hypersurfaces
  • 5. Properties as a toric variety
  • 6. Bundle structure associated with a subset of
  • 7. The case where
  • 8. Existence theorem