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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)
MathSciNet review: 1396959
MSC: Primary 58F17; Secondary 53C22, 58F07

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Table of Contents


  • 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 $M^1$
  • 2. Summing up the local data
  • 3. Structure of $M-M^1$
  • 4. Torus action and the invariant hypersurfaces
  • 5. Properties as a toric variety
  • 6. Bundle structure associated with a subset of $\mathcal {A}$
  • 7. The case where $\#\mathcal {A}=1$
  • 8. Existence theorem