Gauss-Bonnet formulae and rotational integrals in constant curvature spaces

We obtain generalizations of the main result in [10], and then provide geometric interpretations of linear combinations of the mean curvature integrals that appear in the Gauss-Bonnet formula for hypersurfaces in space forms Mλn. Then, we combine these results with classical Morse theory to obtain new rotational integral formulae for the k-th mean curvature integrals of a hypersurface in Mλn.