2022 Fiscal Year Final Research Report
Convexity and global behavior of geodesics on Finsler manifolds
| Project/Area Number |
18K03314
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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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| Review Section |
Basic Section 11020:Geometry-related
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| Research Institution | Fukuoka Institute of Technology |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
永野 哲也 長崎県立大学, 情報システム学部, 教授 (00259699)
糸川 銚 福岡工業大学, 情報工学部, 教授 (90223205)
印南 信宏 新潟大学, 自然科学系, フェロー (20160145)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Keywords | Finsler metric / non-symmetric distance / geodesic / cut locus / conjugate locus / Christoffel symbols |
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| Outline of Final Research Achievements |
Let (M,F) be a complete Finsler n-manifold, n>1. We discuss the preimage of a curve c on M under the exponential map at p. If c does not meet the cut locus of p, then it is clearly lifted in the tangent space at p
via the inverse of the exponential map.However it is not possible if c meets the cut locus of p.
We discuss a curve c intersecting the cut locus of p, where it is conjugate to p. We then develop an idea to extend the exponential map at p beyond the cut locus to p.
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| Free Research Field |
Finsler geometry
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| Academic Significance and Societal Importance of the Research Achievements |
完備フィンスラー多様体の一点pに於ける指数写像がpの切断跡を延長して議論する事によって切断跡の微分可能性について議論出来る様になった点は大きな意義がある。フィンスラー多様体の距離関数が非対称である事に鑑みて
この議論は極めて重要であると考えられる．
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