Related papers: Weierstrass representation for timelike minimal su…
In this paper, following Sullivan, Kusner, and Schmitt, we study conformal immersions of Riemann surfaces into the three-dimensional Euclidean space. Regarding such immersions as special bundle maps from the tangent bundle of the surface to…
A shear-free ray congruence on Minkowski space is a 3-parameter family of null geodesics along which Lie transport of a complementary 2-dimensional spacelike subspace (called the screen space) is conformal. Such congruences are defined by…
We prove a sharp inequality for hypersurfaces in the n-dimensional Anti-deSitter-Schwarzschild manifold for general n greater or equal to 3. This inequality generalizes the classical Minkowski inequality for surfaces in the three…
A canonical normal null direction on a spacelike surface in the four dimensional Minkowski space $\mathbb{R}^{3,1}$ is a parallel vector field $Z$ on $\mathbb{R}^{3,1}$ such that the normal component of $Z$ on the surface is a lightlike…
We define noncommutative minimal surfaces in the Weyl algebra, and give a method to construct them by generalizing the well-known Weierstrass-representation.
Spacelike surfaces in Generalized Robertson-Walker spacetimes whose mean curvature function satisfies a natural nonlinear inequality are analyzed. Several uniqueness and nonexistence results for such compact spacelike surfaces are proved.…
The purpose of this short note is to relate a representation formula due to the Author and P. Romon for Lagrangian surfaces (see math.DG/0009202) to a more general Weierstrass representation type formula found by Konopelchenko for surfaces…
Using the fact that any minimal strongly regular surface carries locally canonical principal parameters, we obtain a canonical representation of these surfaces, which makes more precise the Weierstrass representation in canonical principal…
We introduce canonical coordinates on minimal time-like surfaces in the n-dimensional Minkowski space and prove the existence and the uniqueness of these parameters. With respect to these coordinates the coefficients of the first…
We establish a general formula for the enclosed volume of constant mean curvature (CMC) surfaces in Euclidean three space with translational periods forming a lattice. The formula relates the volume to the surface area, a…
A translation surface in Lorentz-Minkowski space $\rr^3$ is a surface defined as the sum of two spatial curves. In this paper we present a classification of maximal surfaces of translation type. We prove that if a generating curve is…
In this paper, we intend to bring together the hyperbolic spinors, which are useful frameworks from mathematics to physics, and both spacelike and timelike framed curves in Minkowski 3-space $\mathbb{R}_1^3$, which are new type attractive…
In this paper we study curvature types of immersed surfaces in three-dimensional (normed or) Minkowski spaces. By endowing the surface with a normal vector field, which is a transversal vector field given by the ambient Birkhoff…
We obtain improved local well-posedness results for the Lorentzian timelike minimal surface equation. In dimension $d=3$, for a surface of arbitrary co-dimension, we show a gain of $1/3$ derivative regularity compared to a generic equation…
We study semilinear wave equations with Ginzburg-Landau type nonlinearities multiplied by a factor $\epsilon^{-2}$, where $\epsilon>0$ is a small parameter. We prove that for suitable initial data, solutions exhibit energy concentration…
In this paper, using the classifications of timelike and spacelike ruled surfaces, we study the Mannheim offsets of timelike ruled surfaces in Minkowski 3-space. Firstly, we define the Mannheim offsets of a timelike ruled surface by…
Applying the general theory about complete spacelike stationary (i.e. zero mean curvature) surfaces in 4-dimensional Lorentz space $\mathbb{R}^4_1$, we classify those regular algebraic ones with total Gaussian curvature $-\int…
Spacelike surfaces in the Lorentz-Minkowski space L^3 can be endowed with two different Riemannian metrics, the metric inherited from L^3 and the one induced by the Euclidean metric of R^3. It is well known that the only surfaces with zero…
In this paper, we examine timelike loxodromes on three kinds of Lorentzian helicoidal surfaces in Minkowski $n$--space. First, we obtain the first order ordinary differential equations which determine timelike loxodromes on the Lorentzian…
In this study, we deal with the local structure of curves and surfaces immersed in a pseudo-isotropic space I_{p}^{3} that is a particular Cayley-Klein space. We provide the formulas of curvature, torsion and Frenet trihedron in order for…