2009 Fiscal Year Final Research Report
A study of systems of differential equations associated with projectively minimal surfaces
| Project/Area Number |
19540080
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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 |
Geometry
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| Research Institution | Fukui University of Technology |
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Principal Investigator |
SASAKI Takeshi Fukui University of Technology, 自然科学系先端融合研究環, 名誉教授 (00022682)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 射影曲面 / 超幾何微分方程式 / 射影極小曲面 / アフィン球面 / 双曲シュバルツ写像 |
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| Research Abstract |
We defined the flat surfaces in the 3-dimensional hyperbolic space by hypergeometric differential equations and studied the singularities of such surfaces, their dependence on the parameters of the equations and the asymptotic behavior of the surfaces by using the computer algebra and a clarification of the singularities of mappings. We proposed also the definitions of discrete flat surfaces by using some discrete integrable systems. We gave surveys on the study of projective minimal surfaces and proposed research problems on transformation of such surfaces in terms of line congruence and on a study of related differential equations.
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