A century ago, Salkowski [9] introduced a family of curves with constant curvature but non-constant torsion (Salkowski curves) and a family of curves with constant torsion but nonconstant curvature (anti-Salkowski curves). In this paper, we adapt definition of such curves to spacelike curves in Minkowski 3-space. Thereafter, we introduce an explicit parametrization of a spacelike Salkowski curv...

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...

With the help of the Frenet frame of a given pseudo null curve, a family of parametric surfaces is expressed as a linear combination of this frame. The necessary and sufficient conditions are examined for that curve to be an isoparametric and asymptotic on the parametric surface. It is shown that there is not any cylindrical and developable ruled surface as a parametric surface. Also, some inte...

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.

We introduce some new algebraic and topological properties of the Minkowski inverse A([Symbol: see text) of an arbitrary matrix A[Symbol: see text] M m,n (including singular and rectangular) in a Minkowski space μ. Furthermore, we show that the Minkowski inverse A ([Symbol: see text]) in a Minkowski space and the Moore-Penrose inverse A(+) in a Hilbert space are different in many properties suc...

Communicated by Abraham A. Ungar Abstract. In this paper, we investigate the reflections in Minkowski three-space by three different approaches. Firstly, we define Lorentzian reflections with Lorentzian inner product. Then, we examine Lorentzian reflections in view of Lorentzian Householder matrices. Finally, we use pure split quaternions to derive Lorentzian reflections. For each case, we find...

1 Department of Mathematics, Faculty of Sciences, University of Cankiri Karatekin, Cankiri 18100, Turkey 2 School of Mathematics & Statistical Sciences, Arizona State University, Room PSA442, Tempe, AZ 85287-1804, USA 3Department of Mathematics, Faculty of Sciences and Art, University of Kırıkkale, Kırıkkale 71450, Turkey 4University of Kragujevac, Faculty of Science, Department of Mathematics ...

A rotation matrix can be generated by a unit timelike quaternion in the three dimensional Minkowski space. In this paper, we correspond columns of this rotation matrix to Frenet vectors of a nonlightlike curve and we find a reformulation of Frenet’s formulas of nonlightlike curves in terms of the timelike quaternions in the Minkowski 3-space. Moreover, we do same things for the parallel transpo...

Abstract Physics textbooks present Minkowski space as an almost pure mathematical construct, without any explicit restriction on a domain where it is applicable in physics. Meanwhile, its physical meaning cannot but follow the same premises as those which underlies the special relativity theory: motion of free point particles and propagation of electromagnetic waves. However, the common formali...