I read Antonio Ros, Compact Hypersurfaces with Constant Higher Order Mean Curvatures,1987. I don't understand following sentence from the second page 6th line.
From the Gauss equation, we have that if $r$ is even, $H_r$ is a intrinsic invariant of $M$."
Let $\psi : M^n \rightarrow R^{n+1}$ be an orientable hypersurface immersed in Euclidean space, and $k_1, k_2,...,k_n$ be the principal curvatures of the second fundamental form. Define mean curvature of order $r$,$H_r$, by the identity, $$(1+tk_1)(1+tk_2)...(1+tk_n) = 1+\binom{n}{1}H_1{t}+\binom{n}{2}H_2t^2 +...\binom{n}{n}H_nt^n$$
My question is,
why $H_r$ is a intrinsic invariant of M?
