Minimal rotational surfaces in the product space ℚ𝜀2 × 𝕊1

Abstract

In this work, we study minimal rotational surfaces in the product space [Formula: see text], where [Formula: see text] denotes either the unit [Formula: see text]-sphere [Formula: see text] or the [Formula: see text]-dimensional hyperbolic space [Formula: see text] of constant curvature [Formula: see text], according to [Formula: see text] or [Formula: see text], respectively. While there is only one kind of rotational surfaces in [Formula: see text], there are three different possibilities for rotational surfaces in [Formula: see text], 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 [Formula: see text].