GEOMETRY OF LAPLACE OPERATOR OR ITS VARIATION TYPE OPERATOR ON RIEMANNIAN MANIFOLD (2003)

黎曼流形上拉普拉斯算子或其变分型算子的几何结构(2003)

基本信息

批准号：
12640078
负责人：
ISHIKAWA Susumu
金额：
$ 2.37万
依托单位：
SAGA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2003
项目状态：
已结题

项目摘要

We tried to investigate the following themes or questions with concernig of the finite type submanifolds or biharmonic submanifolds :(i)Are there the finite type surfaces with given mean curvature H in the family of surfaces of revolution x.(u, v)=(u cos v, u sin v, f(u)) generated by the periodic function z=f(u) ?(ii)Are there the finite type surfaces with given Gauss curvature K in the family of surfaces of revolution x(u, v)=(u cos v, u sin v, f(u)) generated by the function z=f(u) ?(iii)Are there the finite type surfaces with constant mean curvature in the family of surfaces ?(iv)Are there the Willmore surfaces of finite type ?(v-1)The finite type submanifolds in the space with D` Atri metric.(v-2)The biharmonic submanifolds in the space with D` Atri metricWe will continue to study in future the following still open conjectures of Prof. Bang-yen Chen1.To determine all of the finite type surfaces in Eucldean space of dimension 3(Chen conjectur 1 : The only finite type surfaces in Eucldean space of dimension 3 are the minimal suefaces, spheres and right cylinders.)2.To determine all of the biharmonic submanifolds in Eucldean space of dimension n(Chen conjectur 2 : The only in Eucldean space of dimension n (n>3) are the harmonc ones.)3.To determine all of the biharmonic submanifolds in Minkowsky space of dimension 4.

我们试图对以下主题或问题进行关注，以关注有限类型的子手术或双harmonic submanifolds：（i）是否存在革命表面中给定的平均曲率h的有限类型表面。在革命的表面家族中，x（u，v）=（U cos v，u sin v，f（u））由功能z = f（u）产生？（iii）有限型表面在表面家族中具有平均曲率的持续平均值吗？（iv）是否有有限的有限型表面？带有d'Atri Metricwe的空间中的双谐子延伸物将来将来继续研究以下仍然是对Bang-Yen Chen1教授的开放猜想。确定维度3的Eucldean Space 3中的所有有限型表面（Chen Ixportur 1：Chen Ixportur 1：在Eucldean of Space of Remeldean Space 3中唯一的有限型表面是2. cen sephers cen cen cen cen cen cen cen cen cen cen cen cen seepthe and cen。维度为n的欧几达人空间中的Biharmonic submanifolds（Chen Conjodiur 2：在eucldean空间中唯一的n（n> 3）是Harmonc。