2016 Fiscal Year Final Research Report
Property of super-conformal maps inherited from holomorphic maps and its application
| Project/Area Number |
25400063
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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 |
Geometry
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Research Collaborator |
LESCHKE Katrin University of Leicester, Department of Mathematics, Reader
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | 曲面 / 共形写像 / 超共形写像 / 極小曲面 / ツイスター空間 / 四元数的正則幾何 / 曲面の変換 / 可積分系 |
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| Outline of Final Research Achievements |
A holomorphic function relates a figure in the plane to a figure in the plane
without changing the angle. This is said that a holomorphic function is conformal. A holomorphic function has mathematically good properties.
If a map relates a figure in the plane to a figure in a higher dimensional space, it can be expected that the map has similarly good properties. We speculated that the best realization of this is a super-conformal map to the four dimensional Euclidean space. As a result, a super-conformal map version of a well-known theorem of a holomorphic function such as a super-conformal map version of Schwarz's lemma was proved. These properties are obtained via maps to the twistor space associated with a super-conformal map. We revealed the relation between conformal maps and the maps to the twistor space.
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| Free Research Field |
曲面の微分幾何学
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