Related papers: A method for designing involute trajectory timelik…
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…
In this study, we have obtained the distribution parameter of a ruled surface generated by a straight line in Frenet trihedron moving along a timelike curve and also along another curve with the same parameter. At this time, the Frenet…
In this study, we investigate the existence theorems for timelike ruled surfaces in Minkowski 3-space. We obtain a general system and give the existence theorems for a timelike ruled surface according to Gaussian curvature, distribution…
This work investigates slant timelike-ruled surfaces and their evolute offsets in Minkowski 3-space $\mathbb{E}_{1}^{3}$. Using the symmetry of evolute curves, we derive a parametric formulation for skew timelike-ruled surfaces and…
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…
In this paper, we consider non developable ruled surface with spacelike ruling, timelike ruling, respectively. We give the relations between the structure functions with the curvature and torsion of the striction line of the timelike and…
In this paper, we get the time evolution equations of the curvature and torsion of the evolving spacelike curves in the Minkowski space. Also, we give inextensible evolutions of timelike ruled surfaces that are produced by the timelike…
In this paper, using the classifications of timelike and spacelike ruled surfaces, we define and study the Mannheim offsets of spacelike ruled surfaces in Minkowski 3-space. We give the conditions for spacelike offset surfaces to be…
In this study, we consider the notion of similar ruled surface for timelike and spacelike ruled surfaces in Minkowski 3-space. We obtain some properties of these special surfaces in E_1^3 and we show that developable ruled surfaces in E_1^3…
In this paper, we express surfaces parametrically through a given spacelike (timelike) asymptotic curve using the Frenet frame of the curve in Minkowski 3-space. Necessary and sufficient conditions for the coefficients of the Frenet frame…
We consider spacelike surfaces in the four-dimensional Minkowski space and introduce geometrically an invariant linear map of Weingarten-type in the tangent plane at any point of the surface under consideration. This allows us to introduce…
Isophote comprises a locus of the surface points whose normal vectors make a constant angle with a fixed vector. In this paper, isophote curves are studied on timelike surfaces in Minkowski 3-space E31. The axises of spacelike and timelike…
For a regular curve on a spacelike surface in Lorentz-Minkowski $3$-space, we have a moving frame along the curve which is called a Lorentzian Darboux frame. We introduce five special vector fields along the curve associated to the…
In this paper, we analyze the problem of constructing a surface pencil from a given spacelike (timelike) line of curvature. By using the Frenet frame of the given curve in Minkowski 3-space, we express the surface pencil as a linear…
In this paper, we introduce the dual geodesic trihedron (dual Darboux frame) of a timelike ruled surface. By the aid of the E. Study Mapping, we consider timelike ruled surfaces as dual hyperbolic spherical curves and define the Mannheim…
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 article, we study spacelike and timelike rotational surfaces in a 3--dimensional de Sitter space $\mathbb{S}^3_1$ which are the orbit of a regular curve under the action of the orthogonal transformation of 4--dimensional Minkowski…
In this paper, we define dual geodesic trihedron(dual Darboux frame) of a spacelike ruled surface. Then, we study Mannheim offsets of spacelike ruled surfaces in dual Lorentzian space by considering the E. Study Mapping. We represent…
In this paper, we study Bertrand surface offsets by considering the dual geodesic trihedron(dual Darboux frame) of the ruled surfaces. We obtain the relationships between the invariants of Bertrand trajectory ruled surfaces. Furthermore, we…