Higher Order Willmore Revolution Hypersurfaes in Rn+1
Abstract
Let x : Mn→Nn 1 be an n-dimensional hypersurface immersed in an (n 1)-dimensional Riemannian manifold Nn 1. Let σi (0≤i≤n) be the ith mean curvature and Qn = , where Cin is binomial coefficient. The second author showed that functional Wn(x)=∫MQndM is a conformal invariant and gave the Euler-Lagrange equation. Wn is called the nth Willmore functional of x. A hypersurface is called the nth order Willmore hypersurfaces if it is a solution of the Euler-Lagrange equation. In this paper, we establish the ordinary differential equation of the nth order Willmore revolution hypersurfaces and present standard examples of the nth order Willmore hypersurfaces.References
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