Hypersurfaces with constant scalar curvature in space forms

Let Rn+l(c) be an (n + 1)-dimensional Riemannian manifold with constant sectional curvature c, we also call it space form. When c -1, R"+l(c) = S "+l (i.e. (n + 1)-dimensional unit sphere space); when c = O, Rn+t(c) = E n+l (i.e. (n + 1)-dimensional Euclidean space). Let M be an n-dimensional compact hypersurface in Rn+l(c), and el . . . . . e,, a local orthonormal frame field on M, col . . . . . con its dual coframe field. Then the second fundamental form of M is