Research on submanifold geometry and harmonic map theory in symmetric spaces

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540090
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Osaka City University
• Principal Investigator: OHNITA Yoshihiro 大阪市立大学, 大学院理学研究科, 教授 (90183764)
• Co-Investigator(Kenkyū-buntansha): KATO Shin 大阪市立大学, 大学院理学研究科, 准教授 (10243354)
• Co-Investigator(Renkei-kenkyūsha): SAKAI Takashi 首都大学東京, 大学院理工学研究科, 准教授 (30381445) ; GUEST Martin 早稲田大学, 理工学術院, 教授 (10295470) ; KOIKE Naoyuki 東京理科大学, 理学部, 教授 (00281410) ; TANAKA Makiko S. 東京理科大学, 理工学部, 教授 (20255623)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 部分多様体論 / 極小部分多様体 / ラグランジュ部分多様体 / 対称空間 / 等径超曲面 / 調和写像 / 可積分系

Outline of Final Research Achievements

In this project, from the viewpoints of geometric variational problems, integrable systems, Lie theory, symplectic geometry, we promoted to study harmonic maps in symmetric spaces and integrable systems, Hamiltonian stability of Lagrangian submanifolds, minimal submanifold theory, Lagrangian submanifolds related to isoparametric hypersurfaces, isoparametric submanifolds of finite and infinite dimensions. Especially, we has published our results on the property and structure of compact minimal Lagrangian submanifolds embedded in complex hyperquadrics obtained as the Gauss images of isoparametric hypersurfaces (joint work with Hui Ma), such as the formula of minimal Maslov number, complete determination of Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces and so on. More recently we obtain new results on Hamiltonian non-displaceability of the Gauss images of isoparametric hypersurfaces in another joint work with Hiroshi Iriyeh, Hui Ma and Reiko Miyaoka.

Free Research Field

微分幾何学