Two Classes of Riemannian Manifolds Whose Geodesic Flows are Integrable

Buch | Softcover

143 Seiten

1998
American Mathematical Society (Verlag)
978-0-8218-0640-1 (ISBN)

Infos

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.

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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.

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 30.1.1998
• Reihe/Serie: Memoirs of the American Mathematical Society
• Verlagsort: Providence
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 0-8218-0640-8 / 0821806408
• ISBN-13: 978-0-8218-0640-1 / 9780821806401
• Zustand: Neuware