Study of integrable geodesic flows and related problems
| Project/Area Number |
18K03302
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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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| Review Section |
Basic Section 11020:Geometry-related
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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) |
2018-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 可積分測地流 / ハミルトン力学 / 共役跡 / ラグランジュ特異点 / 射影同値 / C射影同値 / Zoll曲面 / Finsler曲面 / ellipsoid / フィンスラー多様体 / 定フラッグ曲率 / Zoll 曲面 / Finsler 曲面 / 測地線 / リーマン幾何 / リウヴィル多様体 / ケーラー・リウヴィル多様体 |
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| Outline of Final Research Achievements |
A paper with J. Itoh, which was one of the basis of this research, was published on Arnold Math. J., 31-90 (2001) . One of our targets of this research was to extend it to non compact case, and we established the first step by constructing projective embeddings of hyper quadrics into products of spheres.
Next, we studied the PQ equivalence of Topalov on Hermite-Liouville manifolds and gave a generalization of his "PQ-hierarchy". Moreover, we showed that a local inverse of this statement is correct, which would indicate that the notion of PQ equivalence is not so far from that of "C projective equivalence".
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| Academic Significance and Societal Importance of the Research Achievements |
可積分測地流はそれ独自への関心とともに、特異点論、射影同値など他の観点からも興味深い対象となって来ている。本研究は特に共役跡に現れる特異点の問題と、リーマン多様体の射影同値、ケーラー多様体のC射影同値、さらにはエルミート多様体のPQ射影同値に至る一連の概念について、独自の方向を示し、新たな進展をもたらすものである。
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Report
(4 results)
Research Products
(8 results)
