We study helix surfaces with parallel mean curvature vector in Euclidean space from a local point of view. Our main result says that they are either part of a cylinder of revolution or a plane. One way to prove this is with the generalization we found about the Laplacian of a support function of a hypersurface. This allows us to study the constant mean curvature surfaces in space forms which have constant angle with respect to a closed and conformal vector field. The result we find says that these surfaces are totally umbilic.

Helix surfaces in Euclidean spaces / Cadena, Cinthia Barrera; DI SCALA, ANTONIO JOSE'; Ruiz Hernández, Gabriel. - In: BEITRAGE ZUR ALGEBRA UND GEOMETRIE. - ISSN 0138-4821. - STAMPA. - 56:2(2015), pp. 551-573. [10.1007/s13366-014-0226-2]

Helix surfaces in Euclidean spaces

DI SCALA, ANTONIO JOSE';
2015

Abstract

We study helix surfaces with parallel mean curvature vector in Euclidean space from a local point of view. Our main result says that they are either part of a cylinder of revolution or a plane. One way to prove this is with the generalization we found about the Laplacian of a support function of a hypersurface. This allows us to study the constant mean curvature surfaces in space forms which have constant angle with respect to a closed and conformal vector field. The result we find says that these surfaces are totally umbilic.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2642144
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