权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Geometric structures on submanifolds in space forms and differential equations related to their structures.

空间形式子流形上的几何结构以及与其结构相关的微分方程。

基本信息

批准号：
16340020
负责人：
SUYAMA Yoshihiko
金额：
$ 6.2万
依托单位：
Fukuoka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2007
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16340020/
关键词：
conformally flat hypersurface Mobius Geometry warped Product manifold Affine Geometry Kirchhoff elastic rod integrable systems Guichard net variational methods 共形不変量アフィン超球面統計多様体キルヒホッフ弾性捧離散可積分系

项目摘要

(1) Suyama obtained remarkable results in the research on generic conformally flat hypersurfaces. The subject is an open problem since the work by E. Cartan. Suyama and Hertrich-Jeromin (Bath Univ.) constructed all conformally flat hypersurfaces with cyclic Guichard net and gave a complete classification of them by conformal equivalence. This work gives new development in the research on higher dimensional submanifolds from the integrable system view-points.(2) Shiohama studied the relation between radial curvature and topology of warped product manifolds. He gave Alexandrov-Toponogov comparison theorem for various geodesic triangles, and applied it for a classification of warped product manifolds.(3) Kurose studied the method of constructing improper affine hyperspheres and gave a new representation formula and a characterization of the class of improper affine hypersurfaces obtained by this formula.(4) Kurose and Fujioka gave a representation as a Hamiltonian system to the motions of curves in a complex hyperbola associated with the integrable equations of the Burgers hierarchy.(5) Kawakubo studied Kirchhoff elastic rods in three-dimensional space forms, and obtained the explicit formulas for them. Also, he proved that the energy functional for Kirchhoff elastic rods satisfies the Palais-Smale condition. The result gives an effective method of studying the stability of closed Kirchhoff elastic rods.(6) Matsuura studied discretizations of curves and surfaces in connection with the theory of discrete integrable systems. He made a geometric interpretation of the discrete KdV equation, so that he successfully proposed a non-autonomous version of it.

(1)Suyama在一般共形平坦超曲面的研究中取得了显著的成果。自从E.Cartan的工作以来，这个问题一直是一个悬而未决的问题。Suyama和Hertrich-Jeromin(巴斯大学)用循环Guichard网构造了所有共形平坦超曲面，并利用共形等价给出了它们的完全分类。本文从可积系统的角度对高维子流形的研究取得了新的进展。(2)Shiohama研究了翘积流形的径向曲率与拓扑之间的关系。他给出了不同测地三角形的Alexandrov-Toponogov比较定理，并将其应用于翘积流形的分类。(3)Kurose研究了构造广义仿射超球面的方法，给出了由该公式得到的一类广义仿射超曲面的新表示公式和特征。(4)Kurose和Fujioka将曲线在复双曲线中的运动表示为哈密顿系统，并与Burgers族的可积方程相联系。(5)川久保夫研究了三维空间形式的Kirchhoff弹性杆，得到了它们的显式公式。他还证明了Kirchhoff弹性杆的能量泛函满足Palais-Smear条件。这一结果为研究闭合Kirchhoff弹性杆的稳定性提供了一种有效的方法。(6)Matsuura结合离散可积系统理论研究了曲线曲面的离散化。他对离散的KdV方程进行了几何解释，从而成功地提出了它的一个非自治版本。

项目成果

期刊论文数量（46）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Comparison Geometry Referred to Warped Product Manifolds.

比较几何形状参考翘曲产品流形。

DOI：
发表时间：
2006
期刊：
Tohoku Math.J. 58
影响因子：
0
作者：
Y.Mashiko;K.Shiohama
通讯作者：
K.Shiohama

CONFORMALLY FLAT HYPERSURFACES WITH CYCLIC GUICHARD NET

DOI：
10.1142/s0129167x07004138
发表时间：
2007-03
期刊：
International Journal of Mathematics
影响因子：
0.6
作者：
U. Hertrich-Jeromin;Y. Suyama
通讯作者：
U. Hertrich-Jeromin;Y. Suyama

Hadamard-type theorems forhypersurfaces in hyperbolic spaces

双曲空间中超曲面的阿达玛型定理

DOI：
发表时间：
2006
期刊：
Differential Geometry and its Applications 24
影响因子：
0
作者：
L. J. Alias;T. Kurose and G. Solanes
通讯作者：
T. Kurose and G. Solanes

KNOPPIX/Math : Portable and distributable collection of mathematical software and free documents.

KNOPPIX/Math ：便携式和可分发的数学软件和免费文档集合。

DOI：
发表时间：
2006
期刊：
Mathematical Software--ICMS2006. Lecture Notes in Computer Science, 4151, Springer 2
影响因子：
0
作者：
T.Hamada;K.Suzaki;K.Iijima;A.Shikoda
通讯作者：
A.Shikoda

Symplectic volumes of certain symplectic quotients associated with the special unitary group of degree three.

与特殊三阶酉群相关的某些辛商的辛体积。