| Project/Area Number |
20K03595
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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 | Tokai University |
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Principal Investigator |
SABAU SORIN 東海大学, 生物学部, 教授 (80364280)
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| Project Period (FY) |
2020-04-01 – 2024-03-31
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| Project Status |
Completed (Fiscal Year 2023)
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| Budget Amount *help |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2022: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2021: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | Riemannian manifolds / Finsler manifolds / surfaces of revolution / Killing vector fields / the theory of geodesics / cut locus / Zoll metrics / manifold of geodesics / Theory of geodesics / the navigation problem / closed geodesics / flag curvature / geodesics / isometry group / cohomology group / Zoll manifolds / Liouville manifolds / cylinders of revolution / Randers metrics / conjugate locus / theory of geodesics / Cut Locus / Manifolds of geodesics |
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| Outline of Research at the Start |
I will study the projective geometry of the Zoll surfaces and the structure of the cut locus of Finsler manifolds, i.e.
(a)the projective geometry of Zoll structures on spheres, and the geometry of the manifold of geodesics of a Zoll surface endowed with a Finsler structure of constant curvature.
(b)the cut locus structure on special Finsler manifolds, and the relation of the cut locus with the geometrical and topological properties of these Finsler manifolds. In special, the structure of the cut locus of von-Mangoldt surfaces of Finsler type.
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| Outline of Final Research Achievements |
The present research include The study the geometrical and topological properties of Finsler metrics of constant positive flag curvature induced by Zoll metrics, and The study the geometry and topology of Finsler manifolds by using the properties of distance function and the cut locus. Some results are published already,others still in print.
We have determined the local and global behaviour of geodesics, the difference with the Riemannian case and the structure of the cut locus on a Randers surface of revolution.We have performed numerical simulation on computer using the programming language SAGE.
We have studied the cut locus of Randers type metrics on different surfaces of revolution, we have determined the local and global behaviour of geodesics,the structure of the cut locus using a Hamiltonian formalism. The geodesics behaviour and the structure of the cut locus can be explicitly determined in a much more general case than the Zermelo's navigation case with Killing wind.
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| Academic Significance and Societal Importance of the Research Achievements |
Our reseach is important from scientific point of view because it develops more general geometrical concepts than the Riemannian ones showing that the real world is Finslerian.
From social point of view, brings together researchers from Asia and from USA and Europe in international conferences.
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