| Project/Area Number |
09640213
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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 |
解析学
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| Research Institution | Himeji Institute of Technology |
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Principal Investigator |
IWASAKI Chisato Himeji Institute of Technology, Faculty of Sience, Professor, 理学部, 教授 (30028261)
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| Co-Investigator(Kenkyū-buntansha) |
SEKIGUCHI Jiro Himeji Institute of Technology, Faculty of Sience, Professor, 理学部, 教授 (30117717)
UEKI Naomasa Himeji Institute of Technology, Faculty of Sience, Associate Professor, 理学部, 助教授 (80211069)
HOSHIRO Toshihiko Himeji Institute of Technology, Faculty of Sience, Associate Professor, 理学部, 助教授 (40211544)
AKAHORI Takao Himeji Institute of Technology, Faculty of Sience, Professor, 理学部, 教授 (40117560)
UMEDA Tomio Himeji Institute of Technology, Faculty of Sience, Professor, 理学部, 教授 (20160319)
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| Project Period (FY) |
1997 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 1998: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1997: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Keywords | paroboloc differential eqation / fundamental solution / pseudo-differential operator / Riemann Roch theorem / Gauss-Bonnet-Chern theorem / symbolic calculus / curvature of manifold / Kaehler manifold / スペクトル / トッドクラス / リーマン多様体 |
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| Research Abstract |
1. An analytical proof of the local version of the Gauss-Banner-Chern Theorem has been obtained by Chisato Iwasaki in a paper titled A proof of the Gauss Bonnet-Chern Theorem by the symbolic calculus of pseudo-differential operators, only calculating the main term of the fundamental solution for equation of parabolic type, which was constructed by the new method.
2. Applying the above method to manifolds with boundary, we obtained the relation of spectrum of Laplacian and curvatures of manifolds, according to the plan of 1998. This result is one of extension of that of Gunther-Schiminng on manifolds without boundary. This results was tailked in the conference in Germany.
3. Local version of Riemann-Roch Thorem for Kaehler manifolds is obtained, by applying the method of construction of the fundamental solution for the degenerate parabolic equation. This result is presented in both conference at Osaka in 1998 and workshop at Potsdom in 1998.
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