Constructions of helicoidal surfaces by using curvature functions in isotropic space

Abstract

In the present paper, we study helicoidal surfaces in the three dimensional isotropic space $\Bbb I^3$ and construct helicoidal surfaces with prescribed Gaussian curvature or mean curvature given by smooth functions. Moreover, we give some examples of helicoidal surfaces with non-constant Gaussian curvature or mean curvature.