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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

our's theorem and helicoidal surfaces with constant mean curvature in the Bianchi-Cartan-Vranceanu space

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Author(s):
Caddeo, Renzo [1] ; Onnis, Irene I. [1] ; Piu, Paola [1]
Total Authors: 3
Affiliation:
[1] Univ Cagliari, Dipartimento Matemat & Informat, Via Osped 72, I-09124 Cagliari - Italy
Total Affiliations: 1
Document type: Journal article
Source: Annali di Matematica Pura ed Applicata; v. 201, n. 2 AUG 2021.
Web of Science Citations: 0
Abstract

In this paper, we generalize a classical result of Bour concerning helicoidal surfaces in the three-dimensional Euclidean space 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. (AU)

FAPESP's process: 16/24707-4 - Algebraic, geometric and differential topology
Grantee:Daciberg Lima Gonçalves
Support Opportunities: Research Projects - Thematic Grants