2013 Fiscal Year Final Research Report
New directions of research of cut locus and related topics
| Project/Area Number |
23540098
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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 | Kumamoto University |
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Principal Investigator |
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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) |
2011 – 2013
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| Keywords | 測地線 / 最小跡 / 共役跡 / 多面体 |
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| Research Abstract |
This research was separated 5 themes and got progress all themes as the synthetic research. (A) As an extension to general dimension of Jacobi's last statement we could determine the type of its singularities. (B) A main paper of series of studies of the structure of cut locus by using graph theory was accepted. (C) The sensational paper was published which proved by using cut locus that every point on surface is a critical point of distance function from some point. (D) By using cut locus we showed any convex polyhedron is continuously flattened. (E) We construct Finslerian metric with fractal cut locus. In these studies it seems the flattening of polyhedral with cut locus structure is a remarkable new direction of research.
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