An inequality between Willmore functional and Weyl functional for submanifolds in space forms

摘要

Let be an n-dimensional submanifold in an (n + p)-dimensional space form R n+p (c) with the induced metric g. Willmore functional of is , where 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 , where 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 and Weyl funtional ν(g). Keywords Willmore functional - Weyl functional - Inequality Mathematics Subject Classification (2000) 53C42 - 53A10 Communicated by D.V. Alekseevsky.