Abstract
In this paper, we discuss the problem of finding explicit parametrizations for the helicoidal surfaces in a conformally flat 3-space $$\mathbb {E}^3_F$$ with prescribed extrinsic curvature or mean curvature given by smooth functions. Also, we give examples for helicoidal surfaces with some extrinsic curvature and mean curvature functions in $$\mathbb {E}^3_F$$ .
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