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.

Keywords

• Isotropic space,helicoidal surface,mean curvature,Gaussian curvature

References

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