| Project/Area Number |
15540099
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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 | Meijo University |
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Principal Investigator |
HASHIMOTO Hideya Meijo University, School of Science and Technology, Professor, 理工学部, 教授 (60218419)
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| Co-Investigator(Kenkyū-buntansha) |
OZAWA Tetuya Meijo University, School of Science and Technology, Professor, 理工学部, 教授 (20169288)
SEKIGAWA Kouei Niigata University, School of Science, Professor, 理学部, 教授 (60018661)
MASHIMO Kastuya Tokyo University of Agriculture and Technology, School of Technology, Professor, 工学部, 教授 (50157187)
TSUKADA Kaxumi Ochanomizu Women's University, School of Science, Professor, 理学部, 教授 (30163760)
UDAGAWA Seiichi Nihon University, School of Medicine, Assistant Professor, 医学部, 助教授 (70193878)
古田 高士 富山大学, 理学部, 助教授 (40215273)
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| Project Period (FY) |
2003 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 2005: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2004: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2003: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | Exceptional Lie group / Caley algebra / J-holomorphic curves / Grasmann geometry / invariant submanifolds / 概複素構造 / 部分多様体 / 6次元球面 / J-holomorphic curve / 変形 / 6次元球面の概複素構造 / super-minimalな概正則曲線 / 不変部分多様体の変形理論 / 8次元ユークリッド空間内の6次元部分多様体 / spin(7)-frame field |
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| Research Abstract |
Mainly, we study the Grassmann geometry of 6-dimensional sphere. The 6-dimensional sphere has the almost Hermitian structure by taking account of the multiplication of the Cayley algebra. In particular, Hashimoto gives the concrete description of the super-minimal J-holomorphic curves in the 6-dimensional sphere and the formula of Gauss curvature of such J-holomorphic curves. The problem about the existence of the self intersection of the super-minimal J-holomorphic curves were left.
Hashimoto, Taniguchi and Udagawa give the method of construction of all almost complex (J-holomorphic) 2-dimensional Tori of Type (III) in a 5-dimensional sphere which is contained in a 6-dimensional sphere, by taking account of the Theta functions. Also Hashimoto and Sekigawa give the representation of the J-holomorphic curves in the 6-dimensional sphere, which has the cohomogenity one.
Hashimoto and Mashimo studied the 3-dimensional tubes over J-holomorphic curves in the 6-dimensional sphere, whose Kahler angle is constant. This result implies that there are many 3-dimensional totally real, CR-submanifolds in the 6-dimensional sphere.
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