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2017 Fiscal Year Final Research Report

Geometric studies on singularity of non-linear phenomena

Research Project

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Project/Area Number 26287009
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Geometry
Research InstitutionHokkaido University

Principal Investigator

Izumiya Shyuichi  北海道大学, 理学研究院, 特任教授 (80127422)

Co-Investigator(Kenkyū-buntansha) 大本 亨  北海道大学, 理学研究院, 教授 (20264400)
石川 剛郎  北海道大学, 理学研究院, 教授 (50176161)
佐治 健太郎  神戸大学, 理学研究科, 准教授 (70451432)
高橋 雅朋  室蘭工業大学, 工学研究科, 准教授 (80431302)
寺尾 宏明  北海道大学, 国際本部, 特任教授 (90119058)
Co-Investigator(Renkei-kenkyūsha) TONEGAWA Yoshihiro  東京工業大学, 理工学研究科, 教授 (80296748)
ONO Kaoru  京都大学, 数理解析研究所, 教授 (20204232)
UMEHARA Masaki  東京工業大学, 理工学研究科, 教授 (90193945)
KOIKE Shigeaki  東北大学, 理学研究科, 教授 (90205295)
Project Period (FY) 2014-04-01 – 2018-03-31
Keywords非線形現象 / 特異性 / 幾何学 / ラグランジュ特異点 / ルジャンドル特異点
Outline of Final Research Achievements

In this research project we have shown that Lagrangian equivalence among Lagrangian submanifold germs and a certain equivalence relation among the corresponding graph-like wave fronts are the same. Applications of this result include the classical differential geometry, the geometry of the space-time, the differential geometry of singular surfaces and mappings, and so on. On the other hand, a new application of singularity theory to quantum mechanics is also discovered in this research project.

Free Research Field

微分位相幾何学

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Published: 2019-03-29  

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