Helices and helicoidal surfaces

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...

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, ...

On helicoidal ends of minimal surfaces

Helices , Hasimoto Surfaces and B

Travelling wave solutions to the vortex lament ow generated by elastica produce surfaces in R 3 that carry mutually orthogonal foliations by geodesics and by helices. These surfaces are classiied in the special cases where the helices are all congruent or are all generated by a single screw motion. The rst case yields a new characterization for the BB acklund transformation for constant torsion...

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.