ON GENERALIZED LN-SURFACES IN E4

Abstract

The envelopes of one- and two-parameter families of spheres arevery important for applied geometry. A surface M in E4which is consideredas envelopes of its tangent planes are called LN -surface. These surfaces arequadratically parametrized in E4. In the present study we calculate the Gaussian, normal and mean curvatures of these surfaces. Further, we have pointedout the flat and minimal points of the surfaces