| Project/Area Number |
26400066
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
Yamada Kotaro 東京工業大学, 理学院, 教授 (10221657)
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| Co-Investigator(Renkei-kenkyūsha) |
Masaaki Umehara 東京工業大学, 情報理工学院, 教授 (90193945)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | ローレンツ多様体 / ワイエルストラス表現公式 / 特異点 / 極大曲面 / 型変化 / 零平均曲率曲面 / ミンコフスキー空間 / ド・ジッター空間 / CMC-1 面 / 因果特性の変化 / ド・ジッター空間の平均曲率１曲面 / 波面 / ミンコフスキー時空 / 平均曲率 / 折り目特異点 |
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| Outline of Final Research Achievements |
A class of maximal surfaces in Lorentz-Minkowski 3-space, named "Kobayashi surfaces" is introduced. A surface in this class can be extended to a zero-mean curvature surfaces which changes causal types from space-like to time-like. Existence of infinitely many surfaces among this class which are graphs of functions over the space-like plane. On the other hand, the first example of a zero-mean curvature which contains a light-like line and changes causal types across the line is obtained. Such a property, called the light-like line theorem, are generalized for wider class of surfaces.
For a surface in Lorentzian 3-manifold which changes its causal type from space-like to time-like at a light-like point, it is shown that the mean curvature function converges to zero at the light-like point. In particuler, it is shown that a non-zero constant mean curvature surface cannot change its causal type.
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