Variational Problems of Surfaces in a Sphere  

作　　者：Bang Chao YIN 

机构地区：[1]School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2021年第4期657-665,共9页数学学报（英文版）

摘　　要：Let x:M→S^(n+p)(1)be an n-dimensional submanifold immersed in an(n+p)-dimensional unit sphere S^(n+p)(1).In this paper,we study n-dimensional submanifolds immersed in S^(n+p)(1)which are critical points of the functional S(x)=∫_(M)S^(n/2)dv,where S is the squared length of the second fundamental form of the immersion x.When x:M→S^(2+p)(1)is a surface in S^(2+p)(1),the functional S(x)=∫_(M)S^(n/2)dv represents double volume of image of Gaussian map.For the critical surface of S(x),we get a relationship between the integral of an extrinsic quantity of the surface and its Euler characteristic.Furthermore,we establish a rigidity theorem for the critical surface of S(x).

关 键 词：SUBMANIFOLD VARIATION rigidity theorem Euler characteristic 

分 类 号：O186.11[理学—数学]