2017 Fiscal Year Final Research Report
Advanced study of integrable geodesic flows
| Project/Area Number |
26400071
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Okayama University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
伊藤 仁一 椙山女学園大学, 教育学部, 教授 (20193493)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | 測地線 / 可積分測地流 / リウヴィル多様体 / c-projective equivalence / conjugate locus |
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| Outline of Final Research Achievements |
We established a certain development for some problems on "integrable geodesic flows". First, we succeeded enlarging the structure theorem on c-projective equivalence problem to certain degenerate case. Second, we studied the conjugate locus on ellipsoid and Liouville manifolds; we specified the form of singularities arising at branch points and clarified their total shape. Third, we developed the classical result of Staude on the drawing of ellipsoid by pins and thread to Liouville manifolds of any dimension. Fourth, we obtained a Kaehlerian analogue of Eisenhart's theorem concerning the integrability of geodesic flows.
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| Free Research Field |
微分幾何学
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