| Project/Area Number |
12640058
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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 | University of Tsukuba |
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Principal Investigator |
TASAKI Hiroyuki University of Tsukuba, Institute of Mathematics, Associate Professor, 数学系, 助教授 (30179684)
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| Co-Investigator(Kenkyū-buntansha) |
KAWAMURA Kazuhiro University of Tsukuba, Institute of Mathematics, Associate Professor, 数学系, 助教授 (40204771)
HOSHINA Takao University of Tsukuba, Institute of Mathematics, Professor, 数学系, 教授 (00015893)
AIYAMA Reiko University of Tsukuba, Institute of Mathematics, Lecture, 数学系, 講師 (20222466)
NAGATOMO Yasuyuki Kyushu University, Department of Mathematics, Associate Professor, 数理, 助教授 (10266075)
IKAWA Osamu Fukushima National College of Technology, Department of General Education, Assosiate Professor, 一般科, 助教授 (60249745)
保倉 理美 福井大学, 工学部, 助教授 (00191122)
守屋 克洋 筑波大学, 数学系, 助手 (50322011)
東條 晃次 千葉工業大学, 工学部, 講師 (30296313)
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| Project Period (FY) |
2000 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2001: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2000: ¥2,000,000 (Direct Cost: ¥2,000,000)
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| Keywords | homogeneous space / symmetric space / variational problem / integral geometry / Kahler angle / 極小曲面 |
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| Research Abstract |
The head investigator has developed explicit expressions of Poincare integral formulas in order to apply these formulas of integral geometry to variational problems in homogeneous spaces. He has obtained an explicit representa tion of Poincare formula of real surfaces in the complex projective spaces in terms of the Kahler angles of those surfaces. This is the first explicit one in which the integral of intersection numbers is not expressed by the product of the volumes of submanifolds. After this in order to generalize this formula to those for general real submanifolds in the complex projective spaces he defined multiple Kahler angles which were generalizations of Kahler angle. According to the multiple Kahler angle he has developed Poincare formulas of general real submanifolds in the complex projective spaces. As a conse quence a relation among some integrals of the multiple Kahler angles and the volumes of submanifolds can be obtained and will become a tool for variational problems.
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