Developments of nilpotent geometry and nilpotent analysis, and subriemannian geometry

幂零几何和幂零分析以及亚布里曼几何的发展

• 批准号: 16540065
• 负责人: MORIMOTO Tohru
• 金额: $ 2.18万
• 依托单位: Nara Women's University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540065/
• 关键词: nilpotent geometry; nilpotent analysis; subriemannian geometry; Cartan connection; representation of Lie algebra and system of PDEs

We developed nilpotent geometry and nilpotent analysis and applied them to subriemannian geometry. In particular, we have found a simple and general principle which associates systems of partial differential equations to representations of Lie algebras in the framework of nilpotent analysis.We organized the following workshops and symposium :1)Geometry in Nara on Quaternion structures, CR-structures and subriemannian structures, April 12-14,2004 at Nara WU.2)Geometry in Nara around subriemannian geometries, December 13-15,2004 at Nara WU.3)RIMS International symposium "Developments of Cartan geometry and related mathematical problems", October 24-27,2005, at RIMS Kyoto UnivAmong the invited from abroad were D.Alekssevsky, R.Bryant, P.Greiner, R.Montgomery, P.Nurowski, S.H.Wang, I.Zelenko, M.Zhitomirskii. We aimed to further develop nilpotent geometry and nilpotent analysis and to integrate related researches arising world-wide in various countries. The proceedings of the RIMS Symposium soon to appear contain many remarkable results obtained through the symposium.

我们发展了幂零几何和幂零分析，并将它们应用于次黎曼几何。我们组织了以下研讨会和研讨会：1)关于四元数结构、CR结构和次黎曼结构的奈良几何，2004年4月12-14日在奈良举办；2)奈良关于次黎曼几何的几何，2004年12月13-15日在奈良WU；3)RIMS国际研讨会，2005年10月24-27日，在京都大学举行。国外邀请有D.Alekssevsky，R.Bryant，P.Greiner，R.Montgomery，P.Nurowski，首页--期刊主要分类--期刊细介绍--期刊题录与文摘--文摘内容我们的目标是进一步发展幂零几何和幂零分析，并整合世界各国正在兴起的相关研究。即将召开的RIMS研讨会论文集包含了通过该研讨会取得的许多显著成果。

项目成果

Fredholm-Lagrangian-Grassmannian and the Maslov index

Fredholm-Lagrangian-Grassmannian 和 Maslov 指数

• 发表时间: 2004
• 期刊: Journal of Geometry and Physics Vol.51, No.3
• 作者: Y.Agaoka;H.Kaneda;K.Furutani;K.Furutani;G.Ishikawa;Y.Agaoka;森本 徹;森本 徹;T.Morimoto;T.Morimoto;森本 徹;K.Furutani
• 通讯作者: K.Furutani

Local isometric imbeddings of P2(H) and P2(Cay)

P2(H) 和 P2(Cay) 的局部等距嵌入

• 发表时间: 2004
• 期刊: Hokkaido Math.J. Vol.33, No.2
• 作者: Y.Agaoka;E.Kaneda
• 通讯作者: E.Kaneda

Pseudo-differential operator and Reproducing kernels arrising in Geometric quantization

几何量化中出现的伪微分算子和再现核

• 发表时间: 2006
• 期刊: Operator theory Advances and Application 164
• 作者: Y.Agaoka;H.Kaneda;K.Furutani
• 通讯作者: K.Furutani

An example of convex heptagon with Heesch number one

Heesch 数一的凸七边形示例

• 发表时间: 2005
• 期刊: Mem.Fac.Integrated Arts and Sci., Hiroshima Univ., Ser.IV, Science Report 31
• 作者: Y.Agaoka;H.Kaneda;K.Furutani;K.Furutani;G.Ishikawa;Y.Agaoka
• 通讯作者: Y.Agaoka

rigidity of the canonical isometric imbedding of the Quaternion projective plane P^2(H)

四元数射影平面 P^2(H) 的正则等距嵌入的刚性

• 发表时间: 2006
• 期刊: Hokkaido Math. J. 35
• 作者: Y.Agaoka;E.Kaneda
• 通讯作者: E.Kaneda