2009 Fiscal Year Final Research Report
Study of complex analysis from a point of view of parabolic geometry
| Project/Area Number |
18340036
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | The University of Tokyo |
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Principal Investigator |
HIRACHI Kengo The University of Tokyo, 大学院・数理科学研究科, 教授 (60218790)
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| Co-Investigator(Kenkyū-buntansha) |
KOMATSU Gen 大阪大学, 大学院・理学研究科, 准教授 (60108446)
TAKAYAMA Shigeharu 東京大学, 大学院・数理科学研究科, 准教授 (20284333)
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| Research Collaborator |
ROBIN Graham ワシントン州立大学, 数学科, 教授
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| Project Period (FY) |
2006 – 2009
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| Keywords | CR幾何 / 共形幾何 / セゲー核 / アインシュタイン計量 |
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| Research Abstract |
We have given a complete construction of scalar conformal invariants of dimension less than 9 or degree less than 3 ; this was a unsolved problem for even dimensions and is expected to have application to the construction of CR invariants. This result is a consequence of the jet isomorphism theorem that gives a decomposition of the jet space of conformal structures as irreducible tensor spaces ; the isomorphism is defined via the curvature of the ambient metric, a Ricci-flat Lorentz metric associated to conformal structure. On CR geometry, we have formulated an invariant theory that can be applied to describe the Szego kernel.
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