Related problems of cut locus and a generalization of Jacobi's last theorem
| Project/Area Number |
20540085
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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 | Kumamoto University |
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Principal Investigator |
ITOH Jin-ichi Kumamoto University, 教育学部, 教授 (20193493)
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| Co-Investigator(Kenkyū-buntansha) |
KIYOHARA Kazuyoshi 岡山大学, 理学部, 教授 (80153245)
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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 | 幾何学 / 測地線 / 最小跡 / 共役跡 / 第1共役跡 / グラフ / 多面体の折り畳み / 多面体の展開 / Liouviile多様体 / Parallelohedra / 単純閉測地線 / 2次曲面 / Liouville多様体 / 距離関数 / 単純閉擬測地線 / Liouville 多様体 / 鋭角三角形分割 |
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| Research Abstract |
The cut locus of an ellipsoid is an arc on the elliptic coordinate, and the conjugate locus has exactly 4 cusps which is known as Jacobi's last theorem. In this study we determined the cut locus on a general dimensional ellipsoid, and determined the structure of conjugate locus and its singularities. Moreover we studied cut loci of some kind of Liouville manifolds and the relations of cut locus of general surfaces and graphs.
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Report
(4 results)
Research Products
(105 results)
