$q-$spherical surfaces in Euclidean space

Abstract

In this paper we define $q$-spherical surfaces as the surfaces that contain the absolute conic of the Euclidean space as a $q-$fold curve. Particular attention is paid to the surfaces with singular points of the highest order. Two classes of such surfaces, with one and two $n-$fold points, are discussed in detail. We study their properties, give their algebraic equations and visualize them with the program {\it Mathematica}.