**Memoirs of the American Mathematical Society**

1997;
143 pp;
Softcover

MSC: Primary 53; 58;
Secondary 70

Print ISBN: 978-0-8218-0640-1

Product Code: MEMO/130/619

List Price: $50.00

AMS Member Price: $30.00

MAA Member Price: $45.00

**Electronic ISBN: 978-1-4704-0208-2
Product Code: MEMO/130/619.E**

List Price: $50.00

AMS Member Price: $30.00

MAA Member Price: $45.00

# Two Classes of Riemannian Manifolds Whose Geodesic Flows Are Integrable

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*Kazuyoshi Kiyohara*

Two classes of manifolds whose geodesic flows are integrable are defined, and their global structures are investigated. They are called Liouville manifolds and Kähler-Liouville manifolds respectively. In each case, the author finds several invariants with which they are partly classified. The classification indicates, in particular, that these classes contain many new examples of manifolds with integrable geodesic flow.

#### Readership

Graduate students and research mathematicians interested in differential geometry and hamiltonian mechanics.

#### Table of Contents

# Table of Contents

## Two Classes of Riemannian Manifolds Whose Geodesic Flows Are Integrable

- Contents v6 free
- Preface vii8 free
- Part 1. Liouville Manifolds 110 free
- Part 2. Kahler-Liouville Manifolds 8089
- Introduction 8089
- Preliminary remarks and notations 8392
- 1. Local calculus on M[sup(1)] 8392
- 2. Summing up the local data 95104
- 3. Structure of M – M[sup(1) 96105
- 4. Torus action and the invariant hypersurfaces 106115
- 5. Properties as a toric variety 117126
- 6. Bundle structure associated with a subset of A 126135
- 7. The case where #A = 1 133142
- 8. Existence theorem 139148

- References 142151