학술논문
Helicoids and axially symmetric minimal surfaces in 3-dimensional homogeneous spaces.
Document Type
Article
Author
Source
Subject
*GEOMETRY
*MINIMAL surfaces
*RIEMANNIAN manifolds
*SYMMETRIC spaces
*CURVATURE
*GEOMETRIC surfaces
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Language
ISSN
1454-511X
Abstract
The Bianchi-Cartan-Vranceanu spaces are Riemannian 3-manifolds whose isometry groups have at least 4-dimension and not of constant negative curvature. In this paper we study helicoids and axially symmetric minimal surfaces in the Bianchi-Cartan-Vranceanu spaces. In particular, axially symmetric minimal surfaces are explicitly classified in terms of elliptic functions. Moreover the non-existence of totally umbilical surfaces in the irreducible Bianchi-Cartan-Vranceanu spaces is proved. [ABSTRACT FROM AUTHOR]