Some New Characteristic Properties of the A-Pedal Hypersurfaces in En+1

Abstract

The primary purpose of this paper is to present the definition of the a-pedal hypersurface with respect to a point in the interior of a closed, convex and smooth hypersurface M. The secondary purpose of this paper is to give some new characteristic properties of the a-pedal hypersurfaces related to the support function, Gauss curvature, mean curvature, the first and second fundamental forms and their coefficients of M (Section 3). Using the classical methods of the hypersurfaces in differential geometry we have established that the support function h a of the a-pedal hypersurface M a is equal to h(a+1)/P-a where P-a(2=) h(2) + a(2) (III)(del) (h,h).