The Spectral Geometry on the submanifold of (pseudo-) Euclidean space

（伪）欧几里得空间子流形上的谱几何

基本信息

批准号：
09640119
负责人：
ISHIKAWA Susumu
金额：
$ 2.05万
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：
1997
资助国家：
日本
起止时间：
1997 至 1999
项目状态：
已结题

项目摘要

We obtained 25 and more prints in this Project (See REFERENCES).In 19971. We obtained some new results about the classification of biharmonic submanifold in psudo-Euclidean space. In detail,(1) The classification problem of biharmonic curves in psudo-Euclidean space was completed.(2) It was proved that the bihaemonic surfaces do not exist in 3 dimensional psudo-Euclidean space.(3) Some classification theorems of biharmonic surfaces in 4 dimensional psudo-Euclidean space was obtained.2. About the spacelike maximal submanifolds with some conditions for Ricci curvature immersed in de-Sitter sphere in psudo-Euclidean space, the classification of them was discussed.3. About the hypersurfaces of constant scalar curvature immersed in de-Sitter sphere in psudo-Euclidean space, the sphere theorem was discussed.4. About the comformally flat 3 dimensional Riemannian manifolds under some conditions for Ricci curvature and scalar curvature, the classification problem of them was discussed.In 19981. … More We obtained, under some conditions for scalar curvature, that any compact submanifold immersed in de-Sitter sphere in psudo-Euclidean space is only a standard sphere.2. We obtained a characterization about the Clifford torus.3. (1) We discussed about 3-dimensional comformally flat Riemannian manifold with non negative constant scalar curvature and the constan norm of Ricci curvature.(2) We discussed about 3-dimensional comformally flat Riemnnian manifold with negative constant scalar curvature and the constan norm of Ricci curvature.In 19991. We discussed the classification problem about the minimal closed surfaces in unit sphere with bounded norm of Ricci curvature. This result is concerted with the famous theorem by S.S.Chern, do Carmo and S. Kobayashi that the Clifford torus is only minimal closed surfaces of S=n in unit sphere.2. We obtained some progress concerned with the third work of listed in 19983. We now investigate the following open problems proposed by Bang-yen Chen;(1) The classification problem of the finite type surface in 3 Euclidean space.(2) The classification problem of the biharmonic submanifolds in n-dimensional Euclidean space.(3) The classification problem of the biharmonic submanifolds in 4-dimensional Minkovski space. Less

我们在该项目中获得了25张和更多印刷品（参见参考文献）。在19971年。我们获得了有关psudo-euclidean空间中Biharmonic Submanifold分类的一些新结果。详细说明，（1）完成了psudo-euclidean空间中双谐曲线的分类问题。（2）证明，在3个psudo-euclidean space中，双方的表面不存在。（3）在4个dimensions psudo-ecudo-ecudo-ecudean space中，psudean space的一些分类定理均可予以分类。关于浸入psudo-euclidean空间中浸入DE特性球体的RICCI曲率条件的某些条件的间距最大次符号，讨论了它们的分类。3。关于沉浸在psudo-euclidean空间中的DE特性球体中的恒定标态曲率的高度，讨论了球理定理。4。关于在RICCI曲率和标量曲率的某些条件下，Riemannian流形的三个方面的分类问题，讨论了它们的分类问题。我们获得了有关克利福德圆环的特征。3。（1）我们讨论了3维的商品平坦的riemannian流形，具有非负恒定标量曲率和RICCI曲率的康斯坦规范。（2）我们讨论了关于3维相保密的riemnnian歧管，负恒定标量曲率和constan constan corm curvation.in 19991 in Cranfifific in confififien.in in Intrim in confifien.in in Intrim.in Incipifience。 RICCI曲率的有界规范。该结果与S.S. Chern，Do Carmo和S. Kobayashi合作，认为Clifford Torus只是单位球体中S = N的最小闭合表面。2。我们在19983年列出的第三项工作方面取得了一些进展。现在，我们调查了Bang-Yen Chen提出的以下开放问题；（1）在3个欧几里得空间中有限类型表面的分类问题。（2）n维欧亚氏型euclidean Space Biharmonic Submanifolds的分类问题（3）分类。 Minkovski空间。较少的