Higher order Gaussian curvatures of parallel hypersurfaces

Abstract

Let M be a hypersurface in (n+1) -dimensional Euclideanspace $E^{n+1}$and $overline M$ bea parallel hypersurface to M. The higher order Gaussian curvatures of $overline M$ are known ([1], [2]). In this paper we give the higher order Gaussian curvatures of $overline M$ by using its principal curvatures and a new lemma 2.1. Ali GÖRGÜLÜ's paper [5] gives the same results. But he uses a different method. So, our study offers a new and direct method.