Minimal rotational surfaces in the product space ℚ² _ϵ × S¹

In this work, we study minimal rotational surfaces in the product space ℚ² _ϵ × S¹, where ℚ² _ϵ denotes either the unit 2-sphere 2 or the 2-dimensional hyperbolic space ℍ² of constant curvature - 1, according to ϵ = 1 or ϵ = -1, respectively. While there is only one kind of rotational surfaces in S² × S¹, there are three different possibilities for rotational surfaces in ℍ² × S¹, according to the types of the induced inner product on the rotational axis of the surface. We determine the profile curves of all minimal rotational surfaces in ℚ² _ϵ × S¹.