2013 Fiscal Year Final Research Report
Study of Analysis on Manifolds
| Project/Area Number |
23540251
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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 |
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| Co-Investigator(Renkei-kenkyūsha) |
IWASAKI Chisato 兵庫県立大学, 大学院・物質理学研究科, 教授 (30028261)
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| Research Collaborator |
BAUER Wolfram G¨ottingen 大学, 教授
MARKINA Irina Bergen 大学, 教授
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| Project Period (FY) |
2011 – 2013
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| Keywords | sub-Laplacian / sub-Riemann 構造 / 熱核 / Spectral zeta 関数 / ベキ零多様体 / Grushin type 作用素 / Clifford 代数 / 一般ハイゼンベルグタイプ群 |
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| Research Abstract |
(1) We proved that spectral zeta functions on compact nilmanifolds of 2 step are always analytically continued to a meromorphic function with only one simple pole, determined its location formula and gave the residue there together with the ratio by the volume being constant. Also was proved that at the negative integers the function always vanishes. (2) It was proved that among the spheres only on 3, 7 and 15 dimensional spheres, there exists a triviazilable sub-Riemannian structure, especially on 15 dimensional sphere, it was shown that it is of codimension 7. We partly determined the eigenvalues and eigenfunctions for the corresponding sub-Laplacians, including the sub-Laplacian for the codimension 3 case on 7 dimensional sphere. (3) We constructed an action function for a higher step Grushin type operator with two variables in an integral form which is a first step for the construction of the heat kernel for this operator.
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