2005 Fiscal Year Final Research Report Summary
Geometry of the flat tori in the sphere and non- linear wave equations
| Project/Area Number |
15540059
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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 | Utsunomiya University |
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Principal Investigator |
KITAGAWA Yoshihisa Utsunomiya Univ., Faculty of Education, Professor, 教育学部, 教授 (20144917)
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| Co-Investigator(Kenkyū-buntansha) |
SAKAI Kazuhiro Utsunomiya Univ., Faculty of Education, A.P., 教育学部, 助教授 (30205702)
INOGUCHI Jun-ichi Utsunomiya Univ., Faculty of Education, A.P., 教育学部, 助教授 (40309886)
AIHARA Yoshihiro Numazu Collage of Technology, Division of Liberal Arts, P., 教養科, 教授 (60175718)
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| Project Period (FY) |
2003 – 2005
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| Keywords | differential geometry / submanifold / flat torus / isometric deformation / mean curvature / 3-sphere / meromorphic mapping / dynamical system |
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| Research Abstract |
In this research, we studied geometry of flat tori in the 3-sphere, meromorphic mappings, surfaces of constant mean curvature and dynamical systems. The main results of this reseach are summarized as follows.
1.Studies on flat tori in the 3-sphere. In this research, Y.Kitagawa studied the conjecture that any isometric deformation of compact surface in $S^3$ preserves the enclosed volume.
As a result, he proved that the conjecture is ture for all flat tori in $S^3$.
2.Studies on meromorphic mappings. In this research, Y.Aihara proved that for every hypersurface $D$ of degree $d$ in a complex projective space, there exists a holomorphic curve from the complex plane into the projective space whose deficiency for $D$ is positive and less than one.
3.Studies on constant mean curvature surfaces and Backlund transformations. In this research, J.Inoguchi proved that Bianchi-Backlund transformation of a constant mean curvature surface is equivalent to the Darboux transformation and the simple type dressing.
4.Studies on dynamical systems. In this research, K. Sakai proved that the $C^1$ interior of the set of expansive vector fields on a manifold is characterized as the set of vector fields without singularities satisfying both Axiom A and the quasi-transversality condition.
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Research Products
(35 results)
