2017 Fiscal Year Final Research Report
Cross ratio and its falks
| Project/Area Number |
26400065
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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 | The University of Tokyo |
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Principal Investigator |
KANAI Masahiko 東京大学, 大学院数理科学研究科, 教授 (70183035)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | 複比 / パラケーラー構造 |
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| Outline of Final Research Achievements |
The history of cross ratio goes back to ancient Greece. Nevertheless, our understanding on it or its "falks", namely, Schwarzian derivative, para-Kaehler structures and geodesic currents seems quite restrictive. The present research aimed at improve our understanding on them. In particular, starting from para-Kaehler geometry, we discovered new definitions of to the energy of legandrian knots and of the Gauss maps of hypersurfaces of the hyperbolic space. We are going to develop new theories on those new objects in a year or two.
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| Free Research Field |
Geometry
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