2002 Fiscal Year Final Research Report Summary
A study on submanifolds in a complex projective space
| Project/Area Number |
13640061
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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 | Chiba University |
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Principal Investigator |
TAKAGI Ryoichi Chiba Univ., Faculty of Science., Prof., 理学部, 教授 (00015562)
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| Co-Investigator(Kenkyū-buntansha) |
SEKIGAWA Kouei Niigata Univ., Faculty of Science, Prof., 理学部, 教授 (60018661)
SUGIYAMA Kenichi Chiba Univ., Faculty of Science, Asso. Prof., 理学部, 助教授 (90206441)
INABA Takashi Chiba Univ., Faculty of Science., Prof., 理学部, 教授 (40125901)
TOJO Koji Chiba Institute Univ., .Faculty of Science., Lecturer., 自然系, 講師 (30296313)
TSUKADA Kazumi Ochanomizu Univ., Faculty of Science., Prof., 理学部, 教授 (30163760)
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| Project Period (FY) |
2001 – 2002
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| Keywords | cmplex space form / real hypersurface / strongly homogeneous / Lie subgroup / orbit / pricipal curvature / congruent / 分類 |
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| Research Abstract |
Let H be a hyperbolic space form, and G be the group of all isometrics of H. Let K be a Lie subgroup of G. We denote by R the set of points p's in H such that the orbit K(p) of p under K is a real hypersurface in H. We assume that R is not empty, and denote by r the maximal number of the principal curvatures of the orbit K(q), where q ranges over R. Under this situation we obtained Theorem, Assume that r = 3. Then an orbit in H under K is congruent to the well-known model real hypersurface or to the Berndt real hypersurface.
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