1999 Fiscal Year Final Research Report Summary
The application of the Rumin complex to isolated sirgularities
| Project/Area Number |
10640211
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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 | Himeji Institute of Technology |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
MASUDA K INSTITUTION, DEPARTMENT, TITLE OF POSITION Lec., 理学部, 講師 (40280416)
FUJIWARA T INSTITUTION, DEPARTMENT, TITLE OF POSITION Assoc., 理学部, 助教授 (10202293)
IWASAKI Chisato INSTITUTION, DEPARTMENT, TITLE OF POSITION Prof., 理学部, 教授 (30028261)
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| Project Period (FY) |
1998 – 1999
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| Keywords | CR structure / pseudo-convex / isolated singularity |
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| Research Abstract |
Let (v, x) be an isolated singularity in a complex enclidean space CィイD1NィエD1. We consider the intersection of v and the real hypersphere SィイD2εィエD2ィイD12N-1ィエD1(x) (we write M for this intersection). Then M is a non singular real odd dimensional CィイD2NィエD2 manifold. Furthermore, on M, aCR structure is induced from M. This CR structure is of interest. In fact, this CR structure determines the normal isolated singularity. Noting this point, Kuranishi initiated his research on isolated singularities from the point of vie of Cr structures (especially, deformation theory). I followed his line, and in 1981, I succeeded if dimィイD21R ィエD2M=zn-1≧7. But the case dimィイD21R ィエD2M=zn-1≧5 has been left open. Inspired by Rumin's work on contact manifolds, we (with J.M.Lee and Gurfiled constructed a CR version of Rumin's work , and by using the Rumin complex, we settle the case dimィイD21R ィエD2M=zn-1=5. Our complex is efficient in studying the complex structures of isolated singularities from the point of view of Hodge structure. But this is still in preparation.
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