透镜空间

透镜空间是三维流形中非常重要的一类．介绍了透镜空间的三种不同的定义方式,讨论其等价性,并根据三种不同的定义相应地研究透镜空间的基本群、同调群以及同胚等问题．     

环面上U（1）丛的Chern－Simons不变量

讨论环面上Ｕ（１）丛的基本群在ＳＵ（２）中的表示空间，并计算环面上Ｕ（１）丛的平坦ＳＵ（２）－连络的Ｃｈｅｒｎ－Ｓｉｍｏｎｓ不变量。     

非双曲不变环面的初等分支

在相空间中 ,未扰动的n维自治系统 x =F(x)具有一个非双曲闭轨 .利用Floquet理论与平均法 ,讨论在周期扰动下此未扰动系统的非双曲不变环面在扩展相空间中的初等分支 .     

The Morse Index of Wente Tori

We find various lower and upper bounds for the index of Wente tori that contain a continuous family of planar principal curves. We then prove a result that gives an algorithm for computing the index sharply.     

On rigidity of Clifford torus in a unit sphere

We extend the scalar curvature pinching theorems due to Peng-Terng, Wei-Xu and Suh-Yang. Let M be an n-dimensional compact minimal hypersurface in S n+1 satisfying Sf 4 f_3~2 ≤ 1/n S~3 , where S is the squared norm of the second fundamental form of M, and f_k =sum λ_i~k from i and λ_i (1 ≤ i ≤ n) are the principal curvatures of M. We prove that there exists a positive constant δ(n)(≥ n/2) depending only on n such that if n ≤ S ≤ n + δ(n), then S ≡ n, i.e., M is one of the Clifford torus S~k ((k/n)~1/2 ) ×S~...