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The synthetic study by real algebraic geometry, from sub-Riemannian geometry to tropical geometry

实代数几何的综合研究，从亚黎曼几何到热带几何

基本信息

批准号：
22340030
负责人：
GOO Ishikawa
金额：
$ 9.73万
依托单位：
Hokkaido University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2010
资助国家：
日本
起止时间：
2010-04-01 至 2014-03-31
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22340030/
关键词：
tangent surface opening construction open swallowtail open Mond surface open Scherback surface hyperfield Cartan's G2-geometry triality totally singular curve conical control system D-singularity theory null-frontal sub-Riemann met

项目摘要

For singular surfaces associated to integral curves of exterior differential systems related to sub-Riemannian geometry and tropical geometry, we have realized the classification of singularities from real algebraic geometry, and we have completed their generic normal forms. From Legendre duality and control theory, we have classified singularities of tangential varieties to singularities of framed curves and surfaces, we have developed the notion of opening of mappings, and we have applied it to the classification for singularities of tangential varieties to general submanifolds. We have studied G2 sub-Riemannian geometry from non-linear control theory and the representation theory of real algebraic groups, and we have classified the related singularities. Moreover, we have developed the triality of D4 geometry and D4 singularity theory. We have completed the papers for all above themes, all of which already appeared or are under submission in international academic journals.

对于与次黎曼几何和热带几何有关的外微分系统的积分曲线所对应的奇异曲面，我们实现了从真实的代数几何中对奇异点的分类，并完成了它们的通有正规形。从Legendre对偶和控制论出发，我们把切簇的奇点分类为框架曲线曲面的奇点，发展了映射开的概念，并把它应用于一般子流形切簇奇点的分类。本文从非线性控制理论和真实的代数群的表示理论出发，研究了G2次黎曼几何，并对相关的奇性进行了分类。进一步发展了D_4几何的三重性和D_4奇点理论。我们已经完成了上述所有主题的论文，所有这些论文都已经在国际学术期刊上发表或正在提交。

项目成果

期刊论文数量（0）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Generic bifurcations of framed curves in a space form and their envelopes

DOI：
10.1016/j.topol.2011.09.024
发表时间：
2010-02
期刊：
arXiv: Differential Geometry
影响因子：
0
作者：
G. Ishikawa
通讯作者：
G. Ishikawa

Singularities of Tangent Varieties and Differential Systems

切线簇的奇异性和微分系统

DOI：
发表时间：
2011
期刊：
影响因子：
0
作者：
F. Faure;M. Tsujii;Goo Ishikawa;T. Kobayashi;T. Morita;T Ogawa;谷島賢二;M.Izumi;Keisuke Shiromoto;稲生啓行;重川一郎;M.Sasada;Goo Ishikawa
通讯作者：
Goo Ishikawa

Singular path duality for Cartan distributions from geometric control theory (in Japanese)

几何控制理论中嘉当分布的奇异路径对偶性（日语）