Abstract: Let be
the Heisenberg 3-space with Riemannian metric We
study helicoidal surfaces in obtained
by a rotation and translation of a curve around an axis, which does not
intersect the curve. Such a study leads to the evaluation of elliptic integrals.
We give examples of such surfaces with prescribed Gauss curvature.
Keywords and phrases: helicoidal surface, Heisenberg space.