Related papers: Analysis of timelike Thomsen surfaces - with defor…

In the 3-dimensional Lorentz-Minkowski space we prove that the sign of the Gaussian curvature of any timelike minimal surface is determined by the degeneracy and the orientations of the two null curves that generate the surface. Moreover,…

We construct a class of Lorentzian harmonic maps into the de-Sitter $2$-space satisfying the eigenvalue equation $\Box N=2H^2N$ for the d'Alambert operator $\Box$ and a non-zero constant $H$ from framed null curves. We also investigate two…

Minimal surfaces with planar curvature lines in the Euclidean space have been studied since the late 19th century. On the other hand, the classification of maximal surfaces with planar curvature lines in the Lorentz-Minkowski space has only…

We show that to every maximal surface with conelike singularities in Lorentz-Minkowski space $\mathbb{L}^3$ that can be locally represented as the graph of a smooth function, there exists a corresponding timelike minimal surface in…

A timelike minimal surface in Minkowski 3-space is a surface whose induced metric is Lorentzian and with vanishing mean curvature. Such surfaces have many kinds of singularities. In this paper, we prove existence and non-existence theorems…

In this paper, we show the existence of a timelike minimal surface with an arbitrary number of weak complete ends. Then, we discuss the asymptotic behaviour of the simple ends and the topology of the singularity set of the constructed…

We study manifolds with split-complex structure and apply some general results to the study of Lorentz surfaces. In particular, we apply our results to timelike minimal immersions. The conformal realization of these surfaces is obtained…

Minimal surfaces with planar curvature lines are classical geometric objects, having been studied since the late 19th century. In this paper, we revisit the subject from a different point of view. After calculating their metric functions…

We apply the complex analysis over the double numbers $D$ to study the minimal time-like surfaces in $R^4_2$. A minimal time-like surface which is free of degenerate points is said to be of general type. We divide the minimal time-like…

Using techniques of integrable systems, we study a Weierstrass representation formula for timelike surfaces with prescribed mean curvature in Minkowski 3-space. It is shown that timelike minimal surfaces are obtained by integrating a pair…

Isometric class of minimal surfaces in the Euclidean 3-space $\mathbb{R}^3$ has the rigidity: if two simply connected minimal surfaces are isometric, then one of them is congruent to a surface in the specific one-parameter family, called…

We give a comprehensive account of zero mean curvature surfaces in isotropic 3-space with planar curvature lines. After giving a complete classification all such surfaces, we show that they belong to a 1-parameter family of surfaces. We…

In this paper, we consider time-like surfaces in the static space-time given by the warped product $\mathbb L^3_1(c)\, _f\times (I,dz^2)$, where $\mathbb L^3_1(c)$ denotes the Lorentzian space form with the constant sectional curvature…

In the three-dimensional Heisenberg group equipped with a certain left invariant Lorentzian metric, timelike minimal surfaces which have the Abresch-Rosenberg differentials with vanishing multiplication of the coefficient function and its…

The paper focuses on the conformal Lorentz geometry of quasi-umbilical timelike surfaces in the $(1+2)$-Einstein universe, the conformal compactification of Minkowski 3-space realized as the space of oriented null lines through the origin…

Given a constant vector field $Z$ in Minkowski space, a timelike surface is said to have a canonical null direction with respect to $Z$ if the projection of $Z$ on the tangent space of the surface gives a lightlike vector field. In this…

In this paper we introduce the notion of timelike surface with harmonic inverse mean curvature in 3-dimensional Lorentzian space forms, and study their fundamental properties.

In this study we give definitions and characterizations of transversal surfaces of timelike ruled surfaces. We study some special cases such as the striction curve is a geodesic, an asymptotic line or a line of curvature. Moreover, we…

Timelike surfaces in the three-dimensional Heisenberg group with left invariant semi-Riemannian metric are studied. In particular, non-vertical timelike minimal surfaces are characterized by the non-conformal Lorentz harmonic maps into the…

A connected regular surface in Lorentz-Minkowski 3-space is called a mixed type surface if the spacelike, timelike and lightlike point sets are all non-empty. Lightlike points on mixed type surfaces may be regarded as singular points of the…