Abstract
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.
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