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].
In [1], the generalization of Laguerre's function of direction for a surface in ordinary space to a hypersurface of a Riemannian space is obtained. The Laguerre's function of direction for a hypersurface of a Weyl space has been derived in [2]. In this paper, the generalization of Laguerre's function of direction to a hypersurface of generalized Weyl space is made.
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