On the Polar Projection with Respect to Normal Curves

Draw an enveloping hypercone of a fixed hypersphere S from a point P in an n-dimensional projective space Pn and project their points of contact on a fixed hyperplane Pn_ of Pn from a point 0 of S, then we get a hypersphere K in Pni This projection P--JK from Pn to Pn_1 is the so called polar projection with respect to the hypersphere S and plays an important role for discussing the relation between the conformal space and the projective space. As S is a sort of quadratic hypersurfaces, it may be regarded as a highest dimensional algebraic subvariety of the