Bour’s theorem and helicoidal surfaces with constant mean curvature in the Bianchi–Cartan–Vranceanu spaces
Caddeo, RenzoMembro del Collaboration Group
;Onnis, Irene I.;Piu, Paola
2022-01-01
Abstract
In this paper, we generalize a classical result of Bour concerning helicoidal surfaces in the three-dimensional Euclidean space R3 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.File | Dimensione | Formato | |
---|---|---|---|
Bour.pdf accesso aperto
Tipologia: versione editoriale
Dimensione 2.12 MB
Formato Adobe PDF
|
2.12 MB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.