【作者】 李建祥；

【导师】 郭震；

【作者基本信息】 云南师范大学 ， 基础数学， 2008， 硕士

【摘要】 设维黎曼流形Mn到n+1维黎曼流形Nn+1的等距浸入超曲面.设为第i个平均曲率泛函Wn(x)=∫MQndM是共形不变的,称为x的n阶Willmore泛函,满足其极值条件的超曲面称为n阶Willmore超曲面,本文主要考虑了欧氏空间中的高阶Willmore超曲面,给出欧氏空间中n阶Willmore旋转超曲面的微分方程,然后具体给出欧氏空间中一类n阶Willmore超曲面.更多还原

【Abstract】 Let x:M n→Nn+1 be an n-dimensional hypersurface immersed in an (n+1)-dimensional Riemannian manifold Nn+1, Letσi (O≤i≤n)be the ith mean curvature andThe functionalWn(x)=∫MQndM is a conformal invariant, and called nth Willmore functional of x, An extremal hypersurface of conformal invariant functional Wn (x) is called nth order Willmore hypersurface. In this paper we considered the higher order Willmore hypersurface in Euclidean space, We established the ordinary differential equation of nth order revolution Willmore hypersurface, and considered the solution of the O.D.E.. Then we give a classes of nth order Willmore hypersurface in Euclidean space.更多还原