Research on Submanifold Theory via Infinite Dimensional Methods

基于无限维方法的子流形理论研究

• 批准号: 17204006
• 负责人: OHNITA Yoshihiro
• 金额: $ 15.39万
• 依托单位: Osaka City University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2008
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-17204006/
• 关键词: (A)微分幾何; 幾何学; 微分幾何学; 部分多様体; 調和写像; 極小部分多様体; 曲面; 可積分系; モジュライ空間

微分幾何学における部分多様体論は,ガウス以来の歴史の長い学問分野で,常に他の諸分野と関わりながら発展してきた.本研究課題は,有限次元および無限次元リー理論,幾何学的変分問題,可積分系理論,幾何解析等の分野と関わり,伝統的な方法を踏まえ無限次元的手法まで視点を広げて,部分多様体論の研究を広範かつ集中的に組織・推進した.有限次元および無限次元等径部分多様体,ラグランジュ部分多様体のハミルトン変分問題,調和写像と可積分系等を研究推進,新しい方法と結果を与えた.また,この研究領域における国際的な協力体制を整備し,若手研究者たちの活動も大いに促進した.

In differential geometry, the partial manifold theory is divided into two parts: one part is divided into two parts: the other part is divided into two parts. This research topic includes finite dimension theory and infinite dimension theory, differential problems of geometry, theory of integrable systems, geometric analysis, etc., systematic methods, methods of infinite dimension theory, viewpoints, and research on partial multi-dimensional theory. The finite dimension and infinite dimension equal-diameter partial multi-bodies, the transformation problem of partial multi-bodies, the harmonic image writing and the integrable system are studied and promoted, and the new methods and results are discussed. The international cooperation system in this research field is organized, and the activities of researchers are promoted.

项目成果

Moduli spaces of complex Fermi curves and the Willmore functional 数理解析研究所講究録,「部分多様体論のさらなる発展に向けて」

复杂费米曲线的模空间和威尔莫尔数学科学研究所 Kokyuroku，“迈向子流形理论的进一步发展”

• 发表时间: 2006
• 期刊: RIMS 研究集会報告集 1527(in Japanese)
• 作者: 大仁田義裕;乙藤隆史;宇田川誠一
• 通讯作者: 宇田川誠一

Differential geometry of Lagrangian submanifolds and related variational problems, Proceedings of The 12th International Workshop on Differential Geometry and Related Fields

拉格朗日子流形的微分几何及相关变分问题，第十二届微分几何及相关领域国际研讨会论文集

• 发表时间: 2008
• 期刊: Korean Math. Soc. and Research Group in Real and Complex Grassmann Manifolds(ed. by Y. -J. Suh, J. D. Perez, Y. -S. Choi) 12
• 作者: H. Ma;Y. Ohnita;Y. Ohnita;Yoshihiro Ohnita
• 通讯作者: Yoshihiro Ohnita

Differential Geometry of Lagrangian Submanifolds and Hamiltonian Variational Problems

• DOI: 10.1090/conm/542/10702
• 发表时间: 2011
• 作者: Hui Ma;Y. Ohnita

Complex equifocal submanifolds and infinite dimensional anti-Kaehlerian isoparametric submanifolds

复杂等焦子流形和无限维反凯勒等参子流形

• 发表时间: 2005
• 期刊: Tokyo J.Math. 28
• 作者: T. Kumagai;J. Misumi;Naoyuki Koike
• 通讯作者: Naoyuki Koike

Stability and Rigidity of Certain Special Lagrangian Cones

某些特殊拉格朗日锥体的稳定性和刚度

• 发表时间: 2005
• 期刊: Surikaisekikenkyusho Kokyuroku "Differential Geometry and Submanifold Theory" 1460
• 作者: T. Kumagai;J. Misumi;Naoyuki Koike;Y.Ohnita
• 通讯作者: Y.Ohnita