The Weyl Curvature Tensor of Hypersurfaces Under the Mean Curvature Flow

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