HELICOIDAL MINIMAL SURFACES IN A CONFORMALLY FLAT 3-SPACE

Helicoidal Surfaces and Their Gauss Map in Minkowski 3-space

The helicoidal surface is a generalization of rotation surface in a Minkowski space. We study helicoidal surfaces in a Minkowski 3-space in terms of their Gauss map and provide some examples of new classes of helicoidal surfaces with constant mean curvature in a Minkowski 3-space.

Hermite Polynomials And Helicoidal Minimal Surfaces

The main objective of this paper is to construct smooth 1-parameter families of embedded minimal surfaces in euclidean space that are invariant under a screw motion and are asymptotic to the helicoid. Some of these families are significant because they generalize the screw motion invariant helicoid with handles and thus suggest a pathway to the construction of higher genus helicoids. As a bypro...

On helicoidal ends of minimal surfaces

Flat surfaces in the hyperbolic 3-space

In this paper we give a conformal representation of flat surfaces in the hyperbolic 3space using the complex structure induced by its second fundamental form. We also study some examples and the behaviour at infinity of complete flat ends. Mathematics Subject Classification (1991): 53A35, 53C42

Linear Weingarten Helicoidal Surfaces in Isotropic Space

Introduced in 1861 [1], a Weingarten surface in the Euclidean three-dimensional space E3 is a surface M, whose mean curvature H and Gaussian curvature K satisfy a non-trivial relation Φ(H, K) = 0. Such a surface was introduced by Weingarten. The class of Weingarten surfaces is remarkably large, and it consists of intriguing surfaces in the Euclidean space: the constant mean curvature surfaces, ...