| Project/Area Number |
20540077
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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 |
KIYOHARA Kazuyoshi Okayama University, 大学院・自然科学研究科, 教授 (80153245)
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| Co-Investigator(Kenkyū-buntansha) |
ITOU Jinichi 熊本大学, 教育学部, 教授 (20193493)
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| Co-Investigator(Renkei-kenkyūsha) |
IGARASHI Masayuki 東京理科大学, 基礎工学部, 准教授 (60256675)
KATSUDA Atsushi 九州大学, 大学院・数理学研究院, 教授 (60183779)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 可積分測地流 / 楕円体 / 最小跡 / 共役跡 / 半古典近似 / リウヴィル多様体 / 測地線 / カットローカス / Liouville多様体 / Hermite-Liouville様体 / Kaehler-Liouville / Staeckel / cut locus / conjugate locus / ellipsoid |
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| Research Abstract |
We obtained several important results for problems related to integrable geodesic flows. In particular, we determined cut loci and conjugate loci of points for certain class of riemannian manifolds with integrable geodesic flows. Also, we determined the local structure for certain class of hermitian manifolds with integrable geodesic flows. Moreover, we formulated "singular" semiclassical approximation for the laplacian on a certain class of surfaces with integrable geodesic flows.
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