Memoirs of the American Mathematical Society 1997; 143 pp; softcover Volume: 130 ISBN10: 0821806408 ISBN13: 9780821806401 List Price: US$47 Individual Members: US$28.20 Institutional Members: US$37.60 Order Code: MEMO/130/619
 Two classes of manifolds whose geodesic flows are integrable are defined, and their global structures are investigated. They are called Liouville manifolds and KählerLiouville 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 Part 1. Liouville Manifolds  Introduction
 Preliminary remarks and notations
 Local structure of proper Liouville manifolds
 Global structure of proper Liouville manifolds
 Proper Liouville manifolds of rank one
 Appendix. Simply connected manifolds of constant curvature
Part 2. KählerLiouville manifolds  Introduction
 Preliminary remarks and notations
 Local calculus on \(M^1\)
 Summing up the local data
 Structure of \(MM^1\)
 Torus action and the invariant hypersurfaces
 Properties as a toric variety
 Bundle structure associated with a subset of \(\mathcal A\)
 The case where \(\#\mathcal A=1\)
 Existence theorem
