Constructions of helicoidal surfaces by using curvature functions in isotropic space

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Hacettepe Journal of Mathematics and Statistics
Volume:48 Issue:4
Constructions of helicoidal surfaces by using curvature functions in isotropic space

Constructions of helicoidal surfaces by using curvature functions in isotropic space

Authors : Dae Won YOON, Jae Won LEE, Chul Woo LEE

Pages : 959-965

View : 50 | Download : 12

Publication Date : 2019-08-08

Article Type : Research Paper

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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