Ruled surfaces generated by elliptic cylindrical curves in the isotropic space

Abstract In this paper we study the ruled surfaces generated by elliptic cylindrical curves in the isotropic 3-space <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>𝕀</m:mi> <m:mn>3</m:mn> </m:msup> </m:math> {\mathbb{I}^{3}} . We classify such surfaces in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>𝕀</m:mi> <m:mn>3</m:mn> </m:msup> </m:math> {\mathbb{I}^{3}} with constant curvature and satisfying an equation in terms of the components of the position vector field and the Laplacian operator. Several examples are given and illustrated by figures.

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