Study on periodic surfaces using their representations by integrals of conformal one-forms
| Project/Area Number |
22540064
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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 | University of Tsukuba |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
HASEGAWA Kazuyuki 金沢大学, 学校教育系, 准教授 (50349825)
KUROSU Sanae 東京理科大学, 理学部, 助教 (70457844)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 曲面 / 幾何学 / 微分幾何学 / 周期的曲面 / 可積分系 / 変換 / 正則関数 / リーマン面 / 周期 / 閉形式 / クリフォード代数 / 四元数 / 平均曲率一定曲面 / ハミルトン的極小 / ラグランジュ曲面 / 共形 / 積分表示 |
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| Research Abstract |
The correspondence between the Lopez-Ros deformation of a minimal surface in Euclidean (four-)space and the dressing transformations of two families of flat connections associated with a minimal surface was cleared by the joint work with Dr, Katrin Leschke.This result was presented in domestic or foreign conferences and seminars. A generalization of harmonic inverse mean curvature and their transforms was studied. The result was published in an international journal. An analog of the Schwarz lemma for super-conformal surfaces in four-dimenaional Euclidean space is obtained. A preprint about this result was written and submitted to an international journal. Generalizing the Riemann bilinear relation for holomorhphic one-forms, a condition for the existence of periodic surfaces was obtained. A preprint about this result was written and submitted to an international journal.
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Report
(4 results)
Research Products
(29 results)
