Submanifolds of symmetric spaces

对称空间的子流形

• 批准号: 15540075
• 负责人: KIMURA Makoto
• 金额: $ 2.05万
• 依托单位: Shimane 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 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540075/
• 关键词: Symmetric spaces; Submanifolds; Minimality; Special Lagrangian; Austere; 微分幾何学; 極小部分多様体; ラグランジュ部分多様体; 対象空間; Lagrangian

We investigated submanifolds in symmetric spaces, which are considered as a generalization of rules surfaces in 3-dimensional Euclidean space. First we consider submanifolds F which satisfies some good condition in symmetric space M^^〜 and also the space M of such all submanifolds. Then generally we can construct fibre bundle E over M and natural map from E to M^^〜 such that each fiber is mapped bijectively to F. From these object we can construct generalized ruled submanifolds M in M^^〜 from submanifolds Σ in M. In this context, fundamental problem is to study relationship of which M is minimal in M^^〜 and Σ in M. We gave some answers to this problem in some geometrically important cases.On the other hand, we investigated congruence of Frenet curves in complex quadrics by using isoparametric functions on the unit sphere in the tangent space by the joint work with M. Ortega at Granada. Finally we proved fundamental theorem for minimal Lagrangian surfaces in the product of 2-spheres by the joint work with Kaoru Suizu.

研究了对称空间中的子流形，它被认为是三维欧氏空间中规则曲面的推广。首先我们考虑对称空间M^^n中满足某种好条件的子流形F以及所有这样的子流形的空间M。然后一般我们可以构造M上的纤维丛E和从E到M的自然映射，使得每个纤维都双射映射到F。从这些对象出发，我们可以从M^^中的子流形M构造M^^中的广义直纹子流形M。在此背景下，基本问题是研究M在M^^中极小与M在M中极小的关系。另一方面，通过与M.奥尔特加在格拉纳达。最后与水津熏合作证明了2-球面乘积中的极小拉格朗日曲面的基本定理。

项目成果

K.Yokoi: "Bubbly continua and homogeneity"Houston J.Math.. 29. 337-343 (2003)

K.Yokoi：“气泡连续体和同质性”Houston J.Math.. 29. 337-343 (2003)

A class of real hypersurfaces in complex projective space

复射影空间中的一类实超曲面

• 发表时间: 2005
• 期刊: Proc.9th International Workshop on Differential Geometry 9
• 作者: M.Kimura;M.Kimura
• 通讯作者: M.Kimura

Real hypersurfaces some of whose geodesics are plane curves

一些测地线是平面曲线的真实超曲面

• 发表时间: 2005
• 期刊: Tohoku Math.J. 57(to appear)
• 作者: T.Adachi;M.Kimura;S.Maeda
• 通讯作者: S.Maeda

M.Kimura: "Ruled Lagrangian submanifolds in complex projective spaces"Surikaisekiken Kokyuroku. 1346. 155-158 (2003)

M.Kimura：“在复杂射影空间中规则拉格朗日子流形”Surikaisekiken Kokyuroku。

V.A.Chatyrko, Y.Hattori: "Around the equality ind X=Ind X toward to a unifying theorem"Topology Appl.. 131. 295-302 (2003)

V.A.Chatyrko、Y.Hattori：“围绕等式 ind X=Ind X 走向统一定理”拓扑应用 131. 295-302 (2003)