Lorentz流形中的类空超曲面

1.引言在[1]中,Calabi证明了n+1(n≤4)维Minkowski空间中的完备极大类空超曲面是全测地的。在[2]中 , Cheng-Yau对所有的n证明了这一结论。在[3]中,对于某一类Lorentz流形,Nishikawa证明了类似的结果。并且在[2]中,Cheng-Yau还证明了当具有常数平均曲率的类空超曲面M是Minkowski空间的闭子集时,有     

Complete Riemannian Manifold Minimally Immersed in a Unit Sphere S~(+p)(1)

Let M~n be an n-dimensional Riemannian manifold which is minimally immersed ina unit sphere S~(n+p)(1)of dimension n+p.If M~n is compact,then many authors stu-died them and obtained many beautiful results(for examples[1],[2],[3]).Inthis paper,we make use of Yau's a“maximum principle”to extend these results     

拟爱因斯坦流形的一些性质和在其上的拉普拉斯算子的特征值

本文研究了拟爱因斯坦流形的一些性质而且研究了其上的拉普拉斯算子的特征值。从而推广了[1]和[2]的结果。设M是一个n维拟爱因斯坦流形,即R_(ij)=ag_(ij) 6u_iu_j,其中R_(ij)是Ricci张量,a和b是标量函数,u_f是单位向量场。本文用R_(Kji)~t标记黎曼流形的曲率张量。如果▽_m▽_hR_(Kji)~t=▽_h▽_mR_(Kji)~i。称M是S-流形。如果▽_m▽_hR_(ij)=▽_h▽_mR_(ij),我们称M。     

完备λ-超曲面的几何

本文是一篇有关λ-超曲面的综述性文章,讨论了λ-超曲面的构造、稳定性和λ-超曲面的分类以及面积增长.     

RESEARCH ANNOUNCEMENTS Minimally Immersed Hypersurfaces in Spheres With Constant Scalar Curvature

In[1],Chern S.S.,Do Carmo M.and Kobayashi S.proved that Clifford toriare only hypersurfaces minimally immersed in a unit sphere with constant scalar cur-vature R=n(n-1).And Chern S.S.raise the following problem: Consider the set of all compact minimally immersed hypersurfaces in S~(n 1)(1)with constant scalar curvature.Think of the scalar curvatur as a function on thisset.Is the image of this fúnction a discrete set of positive numbers?     

S^4（1）中具有常拟Gauss—Kronecker曲率的超曲面

给出了拟Gauss-Kronecker曲率的定义,并研究了S~4(1)中具有常拟Gauss-Kro-necker曲率的超曲面的特性。