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

Autor(es)

Caddeo, Renzo ^[1] ; Onnis, Irene I. ^[1] ; Piu, Paola ^[1]

Afiliação do(s) autor(es)

^[1] Univ Cagliari, Dipartimento Matemat & Informat, Via Osped 72, I-09124 Cagliari - Italy

• Tipo de documento: Artigo Científico
• Fonte: Annali di Matematica Pura ed Applicata; v. 201, n. 2 AUG 2021.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 16/24707-4 - Topologia algébrica, geométrica e diferencial
• Beneficiário: Daciberg Lima Gonçalves
• Modalidade de apoio: Auxílio à Pesquisa - Temático