The geometry of geodesics and its application to the discrete mathematics
| Project/Area Number |
22540072
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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 | Niigata University |
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Principal Investigator |
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| Project Period (FY) |
2010-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 測地線 / 曲面 / ボロノイ図 / カットローカス / シュタイナー比 / 平面凸ビリヤード問題 / トポノゴフの比較定理 / 球面定理 / リーマン幾何学 / 曲面上の幾何学 / 最小点軌跡 / サブ混合性 / 曲面のボロノイ図 / サブエルゴード性 / 距離関数の差 / 最短ネットワーク / 測地流 / エルゴード性 / 円のリヤード / 最小シュタイナー木 / 測地線の幾何学 / トポノゴフの定理 / コンジュゲートローカス / 極 |
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| Outline of Final Research Achievements |
In an intrinsic metric space, a locally minimizing curve is called a geodesic. We say that a metric space is a geodesic space if any two points can be joined by a minimizing geodesic. H. Busemann put forward the geometry of geodesics in 1955 to study some properties of geodesics, the topological and metric structure of spaces. Using his methods, we produced results on the studies of sets of poles in a Riemannian manifold, the geodesic flows on surfaces and the plane convex billiard ball problems, the Steiner ratio problem for surfaces, a generalization of Toponogov's comparison theorem and some sphere theorems, the relation of a Voronoi diagram and the cut locus. We have a prospect to develop the geometry of geodesics in a non-symmetric intrinsic distance space.
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Report
(6 results)
Research Products
(22 results)
