2010 Fiscal Year Final Research Report
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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| Keywords | 幾何学 / 測地線 / 最小跡 / 共役跡 |
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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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