2013 Fiscal Year Final Research Report
A research on the geometric singularities of non-linear phenomena
| Project/Area Number |
22340011
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Hokkaido University |
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Principal Investigator |
IZUMIYA Shyuichi 北海道大学, 理学(系)研究科(研究院), 教授 (80127422)
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| Co-Investigator(Kenkyū-buntansha) |
ISHIKAWA Goo 北海道大学, 大学院・理学研究院, 教授 (50176161)
TERAO Hiroaki 北海道大学, 大学院・理学研究院, 教授 (90119058)
TONEGAWA Yoshihiro 北海道大学, 大学院・理学研究院, 教授 (80296748)
OHMOTO Toru 北海道大学, 大学院・理学研究院, 教授 (20264400)
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| Co-Investigator(Renkei-kenkyūsha) |
ONO Kaoru 京都大学, 数理解析研究所, 教授 (20204232)
UMEHARA Masaaki 東京工業大学, 大学院・理工学研究科, 教授 (90193945)
KOIKE Shigeaki 東北大学, 大学院・理学研究科, 教授 (90205295)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 特異点 / 非線形現象 / 相対性理論 / ローレンツ空間形 / ルジャンドル特異点 / ラグランジュ特異点 |
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| Research Abstract |
In this research project we constructed the notion of 'lightlike curvature' for spacelike submanifolds of Lorentzian space forms by using the notion of 'lightcone Gauss maps'.As an application of the theory of Legendrian singularities, we described the singularities of the lighhtlike hypersurface along a spacelike submanifold. Moreover, we constructed a geometric framework to describe the caustics of world sheets which is an important notion in the theory of general relativity and the brane world scenario. We clarified the relation of the caustics and the wave front propagations iby using the theory of graph-like Legendrian unfoldings.
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Research Products
(15 results)
