Various geometric structures and Grassmann Geometry

各种几何结构和格拉斯曼几何

• 批准号: 15540099
• 负责人: HASHIMOTO Hideya
• 金额: $ 1.47万
• 依托单位: Meijo University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540099/
• 关键词: Exceptional Lie group; Caley algebra; J-holomorphic curves; Grasmann geometry; invariant submanifolds; 概複素構造; 部分多様体; 6次元球面; J-holomorphic curve; 変形; 6次元球面の概複素構造; super-minimalな概正則曲線; 不変部分多様体の変形理論; 8次元ユークリッド空間内の6次元部分多様体; spin(7)-frame field

Mainly, we study the Grassmann geometry of 6-dimensional sphere. The 6-dimensional sphere has the almost Hermitian structure by taking account of the multiplication of the Cayley algebra. In particular, Hashimoto gives the concrete description of the super-minimal J-holomorphic curves in the 6-dimensional sphere and the formula of Gauss curvature of such J-holomorphic curves. The problem about the existence of the self intersection of the super-minimal J-holomorphic curves were left.Hashimoto, Taniguchi and Udagawa give the method of construction of all almost complex (J-holomorphic) 2-dimensional Tori of Type (III) in a 5-dimensional sphere which is contained in a 6-dimensional sphere, by taking account of the Theta functions. Also Hashimoto and Sekigawa give the representation of the J-holomorphic curves in the 6-dimensional sphere, which has the cohomogenity one.Hashimoto and Mashimo studied the 3-dimensional tubes over J-holomorphic curves in the 6-dimensional sphere, whose Kahler angle is constant. This result implies that there are many 3-dimensional totally real, CR-submanifolds in the 6-dimensional sphere.

我们主要研究六维球面的格拉斯曼几何。考虑到凯莱代数的乘法，6维球体具有几乎埃尔米特结构。特别是，桥本给出了6维球面中超极小J全纯曲线的具体描述以及该J全纯曲线的高斯曲率公式。留下了关于超最小J全纯曲线自交是否存在的问题。Hashimoto、Taniguchi和Udakawa给出了构造所有类型(III)的几乎复杂(J全纯)二维Tori的方法通过考虑 Theta 函数，将 5 维球体包含在 6 维球体中。 Hashimoto和Sekikawa还给出了具有同齐性的6维球面J全纯曲线的表示。Hashimoto和Mashimo研究了6维球面J全纯曲线上的3维管，其卡勒角是恒定的。这个结果意味着在 6 维球体中存在许多 3 维完全真实的 CR 子流形。

项目成果

Submanifolds of a nearly Kahler 6-dimensional sphere

近卡勒 6 维球体的子流形

• 发表时间: 2004
• 期刊: Proceedings of the eighth International workshop on differential geometry 8
• 作者: Hideya Hashimmoto;Kouei Sekigawa
• 通讯作者: Kouei Sekigawa

曲線 幾何学の小径

曲线几何路径

• 发表时间: 2005
• 作者: 小澤 哲也

Deforamations of super-minimal J-holomorphic curves of a 6-dimensional sphere.

6 维球体超最小 J 全纯曲线的变形。

• 发表时间: 2004
• 期刊: Tokyo J. Math 27
• 作者: 橋本 英哉

On some tubes over J-holomorphic curves in S^6

S^6 中 J 全纯曲线上的一些管

• 发表时间: 2005
• 期刊: Tokyo J.Math 28 2
• 作者: 橋本 英哉;問下 克哉
• 通讯作者: 問下 克哉

Constructions of almost complex 2-tori of type (III) in the nearly Kaehler 6-sphere

近凯勒 6 球体中类型 (III) 的近复 2 环结构

• 发表时间: 2004
• 期刊: Differential Geom.Appl 21
• 作者: S.Udagawa;H.Hashimoto;T.Taniguchi
• 通讯作者: T.Taniguchi