2013 Fiscal Year Final Research Report
Various problems concerning integrable geodesic flows
| Project/Area Number |
23540089
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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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| Project Period (FY) |
2011 – 2013
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| Keywords | 可積分測地流 / 楕円体 / 共役跡 / リウヴィル多様体 / C射影同値 |
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| Research Abstract |
We obtained some new results concerning integrable geodesic flows: We clarified the structure of conjugate locus and their singularities on ellipsoids and certain Riemannian manifolds with integrable geodesic flows. In particular, we found that D4+-singularity of Arnold appears at the bifurcation points. Furthermore, we found some intimate relationship between certain Kaehler manifolds with integrable geodesic flows and C-projective equivalence, which seems deeper than usually recognized.
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