2023 Fiscal Year Final Research Report
The projective geometry of Zoll surfaces and the Cut locus on Finsler manifolds
| 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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| Keywords | Riemannian manifolds / Finsler manifolds / surfaces of revolution / Killing vector fields / the theory of geodesics / cut locus / Zoll metrics / manifold of geodesics |
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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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| Free Research Field |
Differential geometry
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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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