New Maximal Surfaces in Minkowski 3-Space with Arbitrary Genus and Their Cousins in de Sitter 3-Space

Caustics of de Sitter spacelike curves in Minkowski 3-space

In this paper, we consider evolutes of spacelike curves in de Sitter 2-space. Applying the theory of singularity theory, we find that these evolutes can be seen as one dimensional caustics which are locally diffeomorphic to lines or ordinary cusps. We establish the relationships between singularities of caustics and geometric invariants of curves under the action of the Lorentz group. c ©2016 A...

Cohomogeneity One Anti De Sitter Space H_1^3

A uniqueness result for maximal surfaces in Minkowski 3-space

In this paper, we study the Dirichlet problem associated to the maximal surface equation. We prove the uniqueness of bounded solutions to this problem in unbounded domain in R. Introduction We consider the Minkowski space-time L3 i.e. R3 with the following pseudoeuclidean metric 〈x, y〉 = x1y1 + x2y2 − x3y3. We define |x| 2 L = 〈x, x〉. A vector is said to be spacelike if |x|2 L > 0 and a surface...

Nonorientable maximal surfaces in the Lorentz-Minkowski 3-space

The geometry and topology of complete nonorientable maximal surfaces with lightlike singularities in the Lorentz-Minkowski 3-space is studied. Some topological congruence formulae for surfaces of this kind are obtained. As a consequence, some existence and uniqueness results for maximal Möbius strips and maximal Klein bottles with one end are proved.

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.