2011 Fiscal Year Final Research Report
A study on global properties of immersed surfaces in space forms from the viewpoint of their Gauss maps
| Project/Area Number |
21740053
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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 | Yamaguchi University (2011)
Kyushu University (2009-2010) |
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Principal Investigator |
KAWAKAMI Yu 山口大学, 大学院・理工学研究科, 講師 (60532356)
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| Project Period (FY) |
2009 – 2011
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| Keywords | ガウス写像 / 値分布 / 波面 / 除外値 / 完備性 / ベルンシュタイン型定理 |
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| Research Abstract |
We investigated value-distribution-theoretic properties of Gauss maps for several classes of immersed surfaces in space forms. In particular, we can obtain the precise maximum for the number of exceptional values of Gauss maps for weakly complete flat fronts in the hyperbolic 3-space and improper affine fronts in the affine 3-space. As an application of this result, a new simple proof of Bernstein type theorems for these classes was provided.
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