Two Classes of Riemannian Manifolds Whose Geodesic Flows are Integrable

Defines two classes of manifolds whose geodesic flows are integrable, and investigates their global structures - they are called Liouville manifolds and Kahler-Liouville manifolds respectively. This work finds several invariants with which they are partly classified.

---

In this work, two classes of manifolds whose geodesic flows are integrable are defined, and their global structures are investigated. They are called Liouville manifolds and Kahler-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.