| Project/Area Number |
12640059
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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, A. P., 教育学部, 助教授 (20144917)
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| Co-Investigator(Kenkyū-buntansha) |
FUJIHIRA Hideyuki Utsunomiya Univ., Faculty of Education, P., 教育学部, 教授 (70114171)
SHIRASOU Takeo Utsunomiya Univ., Faculty of Education, P., 教育学部, 教授 (50007960)
OCHIAI Syoji Utsunomiya Univ., Faculty of Education, P., 教育学部, 教授 (30031545)
AIHARA Yoshihiro Numazu Collage of Technology, Division of Liberal Arts, A. P., 教養科, 助教授 (60175718)
SAKAI Kazuhiro Utsunomiya Univ., Faculty of Education, A. P., 教育学部, 助教授 (30205702)
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| Project Period (FY) |
2000 – 2001
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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 and dynamical systems. The main results of this research are summarized as follows.
(1) Studies on isometric deformations of flat tori in the S-sphere.
In this research, Y. Kitagawa studied isometric deformations of flat tori isometrically immersed in the 3-sphere S^3 with constant mean curvature. As a result, he obtained a classification of the flat tori isometrically immersed in S^3 which admit no isometric deformation.
(2) Studies on algebraic dependence of meromorphic mappings.
In this research, Y. Aihara proved some criteria for the propagation of algebraic dependence of dominant meromorphic mappings from an analytic finite covering space X over the complex m-space into a projective algebraic manifold. Moreover, applying these criteria, he obtained unicity theorems for meromorphic mappings, and gave conditions under which two holomorphic mappings from X into a smooth elliptic curve E are algebraically related.
(3) Studies on vector fields with topological stability.
In this research, K. Sakai (with K. Moriyasu and N. Sumi) gave a characterization of the structurally stable vector fields by making use of the notion of topological stability. More precisely, it was proved that the C^1 interior of the set of all topologically stable C^1 vector fields coincides with the set of all vector fields satisfying Axiom A and the strong transversality condition.
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