A study on global properties of immersed surfaces in space forms from the viewpoint of their Gauss maps
Project/Area Number |
21740053
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Single-year Grants |
Research Field |
Geometry
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Research Institution | Yamaguchi University (2011) Kyushu University (2009-2010) |
Principal Investigator |
KAWAKAMI Yu 山口大学, 大学院・理工学研究科, 講師 (60532356)
|
Project Period (FY) |
2009 – 2011
|
Project Status |
Completed (Fiscal Year 2011)
|
Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
|
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 / 幾何学 / 函数論 / 値分布論 / 島 / 波面(フロント) / 平坦曲面 / 双曲計量 / 非固有アファイン球面 / 平均曲率一定曲面 / 双曲的ガウス写像 / 完全分岐値数 |
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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Report
(4 results)
Research Products
(57 results)