| Project/Area Number |
13640222
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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 |
Global analysis
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
FURUTANI Kenro FURUTANI,Kenro, 理工学部, 教授 (70112901)
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| Co-Investigator(Kenkyū-buntansha) |
KOBAYASHI Takao KOBAYASHI,Takao, 理工学部, 教授 (90178319)
OKA Masatoshi OKA,Masatoshi, 理工学部, 教授 (70120178)
OTSUKI Nbukazu OTSUKI,Nbukazu, 理工学部, 教授 (80112895)
TANAKA Makiko TANAKA,Makiko, 理工学部, 助教授 (20255623)
KOBAYASHI Reido KOBAYASHI,Reido, 理工学部, 教授 (70120186)
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| Project Period (FY) |
2001 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2001: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | Spectral flow / Maslov index / Fredholm operator / symplectic manifold / Polarization / Quaternion Projective spare / Quantization / zeta-regularided determinant / Heisenberg manifold / modified Bessel function / Epstein zeta funtion / 無限積 / Quillen determinant / Maslov line bundle / Caplacian / Mellin transformation / Heat Kernel / スペクトル流 / マスロク指数 / 楕円型微分作用素 / 境界値問題 / Cayley射影平面 / 測地流 / スペクトル逆問題 / product form |
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| Research Abstract |
(1)We proved a splitting formula for a spectral flow of a one parameter family of first order selfadjoint elliptic differential operators which arises when we split a manifold into two components by a hypersurface.To prove this formula we reconstruct a general theory of infinite dimensional Maslov index, where it should be noted that the Maslov index can be defined for arbitrary paths as an intersection number with a Maslov cycle by means of a functional 'analytic method.We also proved a reduction theorem of the Maslov index in the infinite dimension(2)We found the complexified Hopf fiberation on the punctured cotangent bundle of the quaternion projective space, and constrict two quantization operators of the geodesic flow on quaternion projective spaces by two methods.(3)We construct a Kahler structure on the punctured cotangent bundle of the Cayley projective plain whose Kahler form coincides with the natural symplectic form.This is given by explicitly embedding it into the space of 8×8 complex matrices.(4)We proved an integral representation of the zeta-regularized determinant of 3 and 4 dimensional Heisenberg manifolds, and also give a general formula for product type Romanian manifolds.Then we apply the formula to give an expression for the zeta-regularized determinant of the higher dimensional torus.
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