2011 Fiscal Year Final Research Report
Researches of principal distributions and over-determined systems on surfaces
| Project/Area Number |
21740054
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Kumamoto University |
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Principal Investigator |
ANDO Naoya 熊本大学, 大学院・自然科学研究科, 准教授 (50359965)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 曲面 / 主分布 / 優決定系(過剰決定系) / 準曲面 |
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| Research Abstract |
I characterized minimal surfaces in E^3 in terms of over-determined systems on surfaces. I devised two generalizations of an over-determined system on a surface and obtained several results which are considered as generalizations of results I already had with respect to over-determined systems on surfaces. I presented another proof of a result by Koiso-Palmer with respect to surfaces with constant anisotropic mean curvature. I locally represented principal distributions on a surface as fields obtained from eigendirections of the Hessian of some function with respect to the first fundamental form of the surface.
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