# Two Classes of Riemannian Manifolds Whose Geodesic Flows Are Integrable

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*Kazuyoshi Kiyohara*

#### 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