2004 Fiscal Year Final Research Report Summary
Submanifolds of symmetric spaces
| Project/Area Number |
15540075
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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 | Shimane University |
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Principal Investigator |
KIMURA Makoto Shimane Univ., Interdisciplinary Faculty of Sci.Eng., Professor, 総合理工学部, 教授 (30186332)
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| Co-Investigator(Kenkyū-buntansha) |
HATTORI Yasunao Shimane Univ., Interdisciplinary Faculty of Sci.Eng., Prof., 総合理工学部, 教授 (20144553)
MAEDA Sadahiro Shimane Univ., Interdisciplinary Faculty fo Sci.Eng., Prof., 総合理工学部, 教授 (40181581)
YOKOI Katsuya Shimane Univ., Interdisciplinary Faculty of Sci.Eng., Ass.Prof., 総合理工学部, 教授 (90240184)
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| Project Period (FY) |
2003 – 2004
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| Keywords | Symmetric spaces / Submanifolds / Minimality / Special Lagrangian / Austere |
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| Research Abstract |
We investigated submanifolds in symmetric spaces, which are considered as a generalization of rules surfaces in 3-dimensional Euclidean space. First we consider submanifolds F which satisfies some good condition in symmetric space M^^〜 and also the space M of such all submanifolds. Then generally we can construct fibre bundle E over M and natural map from E to M^^〜 such that each fiber is mapped bijectively to F. From these object we can construct generalized ruled submanifolds M in M^^〜 from submanifolds Σ in M. In this context, fundamental problem is to study relationship of which M is minimal in M^^〜 and Σ in M. We gave some answers to this problem in some geometrically important cases.
On the other hand, we investigated congruence of Frenet curves in complex quadrics by using isoparametric functions on the unit sphere in the tangent space by the joint work with M. Ortega at Granada. Finally we proved fundamental theorem for minimal Lagrangian surfaces in the product of 2-spheres by the joint work with Kaoru Suizu.
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