Constructions of helicoidal surfaces by using curvature functions in isotropic space

Year 2019, Volume: 48 Issue: 4, 959 - 965, 08.08.2019

Dae Won Yoon Jae Won Lee Chul Woo Lee

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.

Keywords

Isotropic space, helicoidal surface, mean curvature, Gaussian curvature

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