| Project/Area Number |
17K05222
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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 | Sugiyama Jogakuen University |
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Principal Investigator |
Itoh Jin-ichi 椙山女学園大学, 教育学部, 教授 (20193493)
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| Co-Investigator(Kenkyū-buntansha) |
清原 一吉 岡山大学, 自然科学研究科, 特命教授 (80153245)
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| Project Period (FY) |
2017-04-01 – 2024-03-31
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| Project Status |
Completed (Fiscal Year 2023)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 最小跡 / 測地線 / 第一共役跡 / 距離関数 / 多面体 / 全曲率 / 最少跡 / 第１共役跡 |
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| Outline of Final Research Achievements |
As a comprehensive study on the cut locus, we conducted a well-balanced study in the following five areas. (A) A paper on the generalization of Jacobi's Last Theorem was published. (B) For the study of the structure and properties of cut loci, we defined the minimum traces of general polyhedra and the minimum traces of graphs. (C) Interesting results have been published in the study of problems related to cut locus (farthest point sets, pseudogeodesics, critical points of distance functions, etc.), and new problems and developments have continued. (D) The problem of applying the cut locus was to characterize cells with peculiar shapes. (E) As for the consideration of the cut locus in other related metrics, some time is now needed to obtain the results.
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| Academic Significance and Societal Importance of the Research Achievements |
最小跡の研究は20世紀初頭のポアンカレの論文によって始まり，その後の長い研究の歴史がある．それの進展に貢献するものといえる．また，楕円面上の測地線の挙動からその第一共役跡の特異点に関してはヤコビの最終定理として知られており，それの一般次元への拡張を与えたことになる．
応用面に関しても，多面体の unfolding や Volonoi分割等の計算機科学との関連があり，また，本研究中に始めた，特異形状の細胞を特徴付けるのにも将来的に役立つ可能性があり意義深いと思われる．更に，定義が単純であることから数学教育の分野にもその有用性が期待される．
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