Global studies of principal distributions on surfaces and researches of principal distributions on various submanifolds
| Project/Area Number |
24740048
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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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, 自然科学研究科, 准教授 (50359965)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 主分布 / 過剰決定系 / 整合条件 / 平均曲率ベクトルが零 / 複素曲線 / 正則３次微分 / アファインSchwarz写像 / 球面Schwarz写像 / 極小曲面 / 多項式型の過剰決定系 / ４次元de Sitter空間 / 平均曲率ベクトル（が零である） / 共形Gauss写像 / Willmore曲面 / 光的な法ベクトル場 / 曲率線 / 測地線 / 一定平均曲率 |
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| Outline of Final Research Achievements |
Referring to results of over-determined systems on surfaces in the Euclidean space, I obtained the corresponding results of over-determined systems on surfaces in the other 3-dimensional space forms. I obtained characterizations of spacelike surfaces with zero mean curvature vector in the 4-dimensional Riemannian and Lorentz space forms in terms of the induced metrics and principal distributions w.r.t. suitable normal vector fields. A minimal surface in the 4-dimensional Euclidean space s.t. principal curvatures do not depend on the choice of a unit normal vector is congruent with a complex curve in the two-dimensional complex number space and characterized in terms of the induced metric and a holomorphic cubic differential. In relation to this characterization, any complex curve is locally considered as the image of the composition of an affine Schwarz map and a parallel translation. I obtained a characterization of a sphere Schwarz immersion in terms of a positive-valued function.
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Report
(4 results)
Research Products
(24 results)
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[Journal Article] Over-determined systems on surfaces2014
Author(s)
Naoya Ando
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Journal Title
``Differential Geometry of Submanifolds and its Related Topics'', Proceedings of the international Workshop in Honor of S. Maeda's 60th Birthday
Volume: なし
Pages: 273-287
Related Report
Peer Reviewed
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