Fourth fundamental form and i-th curvature formulas in E4

Abstract

We introduce fourth fundamental form IV, and i-th curvature formulas of hypersurfaces in the four dimensional Euclidean geometry E-4. Defining fourth fundamental form and i-th curvatures for hypersurfaces, we calculate them on rotational hypersurface. In addition we study rotational hypersurface satisfying Delta(IV)x = Ax for some 4x4 matrix A.