On convolution surfaces in Euclidean 3-space

Abstract

In the present paper we study with the convolution surface C = M N of a paraboloid M ⊂ E 3 and a parametric surface N ⊂ E 3 . We take some spacial surfaces for N such as, surface of revolution, Monge patch and ruled surface and calculate the Gaussian curvature of the convolution surface C. Further, we give necessary and sufficient conditions for a convolution surface C to become flat.