2017 Fiscal Year Final Research Report
Geometry of geodesics for spaces with non-symmetric distances
| Project/Area Number |
15K13435
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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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) |
2015-04-01 – 2018-03-31
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| Keywords | 測地線 / リーマン幾何学 / フィンスラー幾何学 / 非対称距離の幾何学 / カット―ローカス / 平行線の理論 / 測地円の漸近挙動 / ブーズマン関数 |
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| Outline of Final Research Achievements |
A geodesic space is a metric space where geodesics are defined.Geometry of geodesics provides tools to study the topological and geometrical structure of geodesic spaces. Riemannian geometry, Finsler geometry and Alexandrov geometry are those examples.It is not studied systematically the space where distance is non-symmetric in that while it is always interested.I studied each property and theorem known in the symmetric case to get their generalizations and new results in the non-symmetric case by geometry of geodesics.I announced those result as some articles.
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| Free Research Field |
測地線の幾何学
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