Generalization of Wente torus in complex spaces forms
| Project/Area Number |
21540061
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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 | Tohoku University |
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Principal Investigator |
KENMOTSU Katsuei 東北大学, 大学院・理学研究科, 名誉教授 (60004404)
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| Project Period (FY) |
2009 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 微分幾何学 / 平均曲率一定曲面 / 平均曲率ベクトル / 平行平均曲率ベクトル / ウエンテトーラス / 平均曲率 一定曲面 / 平行平均曲率ベクトル場 / 複素空間形 / トーラス |
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| Research Abstract |
Parallel mean curvature vector surfaces in complex space forms are studied. It is proved that, when the codimension of the immersion is two, the set of such surfaces is divided in two families, which are called cmc type and general type. The surface of cmc type depends on one real valued harmonic function and the one of general type, if it exists, depends on two independent real valued functions. Related to the theory of constant mean curvature surfaces, we studied also rotational surfaces with periodic mean curvature. In order to extend the research to higher dimension, we proved the existence theorem of rotational hypersurfaces with prescribed mean curvature function.
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Report
(5 results)
Research Products
(26 results)
