03228nam 2200577 450 991081188940332120170822144357.01-4704-0208-4(CKB)3360000000464803(EBL)3114543(SSID)ssj0000889282(PQKBManifestationID)11482815(PQKBTitleCode)TC0000889282(PQKBWorkID)10876593(PQKB)10964761(MiAaPQ)EBC3114543(RPAM)1181647(PPN)195415035(EXLCZ)99336000000046480319970716h19971997 uy| 0engur|n|---|||||txtccrTwo classes of Riemannian manifolds whose geodesic flows are integrable /Kazuyoshi KiyoharaProvidence, Rhode Island :American Mathematical Society,[1997]©19971 online resource (159 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 619"November 1997, volume 130, number 619 (third of 4 numbers)."0-8218-0640-8 Includes bibliographical references (pages 142-143).""Contents""; ""Preface""; ""Part 1. Liouville Manifolds""; ""Introduction""; ""Preliminary remarks and notations""; ""1. Local Structure of Proper Liouville Manifolds""; ""1.1. Liouville manifolds and the properness""; ""1.2. Infinitesimal structure at a point in M[sup(s)]""; ""1.3. Local structure around a point in M[sup(s)]""; ""1.4. Proof of Lemma 1.2.7""; ""2. Global Structure of Proper Liouville Manifolds""; ""2.1. Submanifolds J""; ""2.2. Admissible submanifolds""; ""2.3. The core of a proper Liouville manifold""; ""3. Proper Liouville Manifolds of Rank One""""3.1. Configuration of zeros and type of cores""""3.2. Possible cores""; ""3.3. Constructing a Liouville manifold from a possible core""; ""3.4. Classification""; ""3.5. Isomorphisms and isometries""; ""3.6. C[sub(2)]Ï€-metrics""; ""Appendix. Simply Connected Manifolds of Constant Curvature""; ""A.1. Possible cores""; ""A.2. The sphere S[sup(n)]""; ""A.3. The euclidean space R[sup(n)]""; ""A.4. The hyperbolic space H[sup(n)]""; ""Part 2. Kahler-Liouville Manifolds""; ""Introduction""; ""Preliminary remarks and notations""; ""1. Local calculus on M[sup(1)]""; ""2. Summing up the local data""""3. Structure of M â€? M[sup(1)""""4. Torus action and the invariant hypersurfaces""; ""5. Properties as a toric variety""; ""6. Bundle structure associated with a subset of A""; ""7. The case where #A = 1""; ""8. Existence theorem""; ""References""Memoirs of the American Mathematical Society ;no. 619.Geodesic flowsRiemannian manifoldsGeodesic flows.Riemannian manifolds.510 s516.3/73Kiyohara Kazuyoshi1954-1607390MiAaPQMiAaPQMiAaPQBOOK9910811889403321Two classes of Riemannian manifolds whose geodesic flows are integrable3933640UNINA