Two classes of Riemannian manifolds whose geodesic flows are integrable
Author(s)
Bibliographic Information
Two classes of Riemannian manifolds whose geodesic flows are integrable
（Memoirs of the American Mathematical Society, no. 619）
American Mathematical Society, 1997
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"November 1997, volume 130, number 619 (third of 4 numbers)." -- t.p.
Includes bibliographical references
Description and Table of Contents
Description
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.
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. Kahler-Liouville manifolds: Introduction Preliminary remarks and notations Local calculus on $M^1$ Summing up the local data Structure of $M-M^1$ Torus action and the invariant hypersurfaces Properties as a toric variety Bundle structure associated with a subset of $\mathcal A$ The case where $ No. \mathcal A=1$ Existence theorem.
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