Author:
Caddeo Renzo,Onnis Irene I.,Piu Paola
Abstract
AbstractIn this paper, we generalize a classical result of Bour concerning helicoidal surfaces in the three-dimensional Euclidean space $${\mathbb {R}}^3$$
R
3
to the case of helicoidal surfaces in the Bianchi–Cartan–Vranceanu (BCV) spaces, i.e., in the Riemannian 3-manifolds whose metrics have groups of isometries of dimension 4 or 6, except the hyperbolic one. In particular, we prove that in a BCV-space there exists a two-parameter family of helicoidal surfaces isometric to a given helicoidal surface; then, by making use of this two-parameter representation, we characterize helicoidal surfaces which have constant mean curvature, including the minimal ones.
Funder
Università degli Studi di Cagliari
Publisher
Springer Science and Business Media LLC
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