WEYL CURVATURE TENSOR OF HYPERSURFACES UNDER THE MEAN CURVATURE FLOW

Abstract

In this paper we study the evolution of Weyl curvature tensor of
hypersurfaces in $R^{n+1}$ under the mean curvature flow. We find a bound for the Weyl curvature tensor of hypersurface during the evolution in term of time. As a consequence, we suppose that the initial hypersurface is conformally flat i.e. W = 0 at t = 0, then we find an upper estimate for W during the evolution in term of time.