1998 Fiscal Year Final Research Report Summary
| Project/Area Number |
09640111
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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 | OKAYAMA UNIVERSITY |
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Principal Investigator |
IKEDA Akira FACULTY of EDUCATION,OKAYAMA UNIVERSITY,PROFESSOR, 教育学部, 教授 (30093363)
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| Co-Investigator(Kenkyū-buntansha) |
AGAOKA Yoshio HIROSHIMA UNIVERSITY,FACULTY OF INTEGRATED ARTS AND SCIENCES,ASSOCIATE PROFESSOR, 総合科学部, 助教授 (50192894)
MASHIMO Katsuya TOKYO UNIVERSITY OF AGULICULTURE AND TECHNOLOGY,DEPARTMENT of MATHEMATICS,ASSOCI, 工学部, 助教授 (50157187)
KATSUDA Atsushi FACULTY OF SCIENCES,ASSOCIATE PROFESSOR, 理学部, 助教授 (60183779)
URAKAWA Hajime TOHOKU UNIVERSITY,GRADUATE SCHOOLE OF INFORMATION SCIENCES,PROFESSOR, 大学院・情報科学研究科, 教授 (50022679)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Dirac operator / Spin structure / isospectral problem / spherical space forms / spectral zeta functions / Laplacian for graphs |
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| Research Abstract |
1. We construct some examples of Dirac isospectral lens spaces containing 17 dimensional ones. To construct Dirac isospectral lens spaces, we study the first series of Laplace 0-isospectral lens spaces given by the author. By computing the Poincare series associated to the Dirac spectrum of these lens spaces, we determine which lens spaces are Dirac isospectral or not. We also determine our Dirac isospectral lens spaces are Laplace p-isospectral or not.
2. Let M be a compact connected Riemannian manifold, DELTA^p_ the Laplacian acting on the space of smooth p-forms on M.Let zeta^<p, delta>_(s) be the spectral zeta function associated to the spectrum of delta-closed p-forms. We study a zeta^<p, delta>_(s) for the standard spheres with constant curvature 1 and zeta_M(s) for a compact simply connected Riemannian symmetric spaces of rank 1. We give residues of thier spectral zeta functions explicitely which have very simple forms. Moreover we give a proof zeta^<p, delta>_<D22n+1@>D2> (s) vanises at negative integers.
3, We give estimates of Green kernels and Heat kernels for infinite graphs, moreover we give an sharp estimete of Green kernels and Heat kernels for some infinite regular graphs.
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