AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution

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: https://doi.org/10.1090/memo/0619
MathSciNet review: 1396959
MSC: Primary 58F17; Secondary 53C22, 58F07

View full volume as PDF

Read more about this volume

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 $M^1$
• 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