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