科研之友
微信
新浪微博
Facebook
分享链接
摘要
Let phi : M -> Rn p(c) be an n-dimensional submanifold in an (n p)-dimensional space form Rn p(c) with the induced metric g. Willmore functional of phi is W(phi) = integral(M)(S - nH(2))(n/2)dv, where S = Sigma(alpha, i, j) (h(ij)(alpha))(2) is the square of the length of the second fundamental form, H is the mean curvature of M. The Weyl functional of (M, g) is nu(g) = integral(M) |W-g|(n/2)dv, where |W-g|(2) = Sigma(i, j, k, l) W-ijkl(2) and W-ijkl are the components of the Weyl curvature tensor W-g of ( M, g). In this paper, we discover an inequality relation between Willmore functional W(phi) and Weyl funtional nu(g).
