2016 Fiscal Year Final Research Report
An advanced study of cut locus and related topics
| Project/Area Number |
26400072
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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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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | 測地線 / 最小跡 / 共役跡 / 多面体 |
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| Outline of Final Research Achievements |
This research of cut locus was separated 5 themaes and developed all themaes synthetically. (A) As an extension of Jacobi's last statement in general dimension, we finished the paper and submitted it. As a thread construction of quadric surface, we published the paper. (B) A main paper of series of studies of the structure of cut locus by using graph theory was published. (C) We almost finished the paper of the relation between the number of distance functions such that a point is critical and the topology of orientable surface. (D) We discussed continuous flattening of non-convex polyhedral surface by using cut locus, but we firstly got the result by the other method. (E) We published the paper constructing the Finslerian metric with fractal cut locus.
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| Free Research Field |
幾何学
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