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In this paper we study the ruled surfaces generated by elliptic cylindrical curves in the isotropic 3-space  3{\mathbb{I}^{3}}   . We classify such surfaces in  3{\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.

Ruled surfaces generated by elliptic cylindrical curves in the isotropic space