Related papers: Non-Null Weakened Mannheim curves
In this paper, we investigate Mannheim pairs, Frenet-Mannheim curves and Weakened Mannheim curves with respect to the modified orthogonal frame in Euclidean 3-space(E 3 ). We obtain some characterizations of these curves.
In this paper, we give the characterizations of Mannheim Partner Curves in Minkowski 3-space . Firstly, we classify these curves in . Next, we give some relationships characterizing these curves and we show that Mannheim theorem is not…
In this paper, we investigate the similarity transformations in the Minkowski-n space. We study the geometric invariants of non-null curves under the similarity transformations. Besides, we extend the fundamental theorem for a non-null…
In this paper, we firstly introduce the group of similarity transformations in the Minkowski-3 space. We describe differential- geometric invariants of a non-lightlike curve according to the group of similarity transformations of the…
In this paper, we give the definition of the natural mate of a non-null Frenet curve in Minkowski 3-spaces. The main purpose of this paper is to prove some relationships between a non-null Frenet curve and its natural mate. In particular,…
We derive Frenet-type results and invariants of spatial curves immersed in $3$-dimensional generalized Minkowski spaces, i.e., in linear spaces which satisfy all axioms of finite dimensional real Banach spaces except for the symmetry axiom.…
The presented paper is devoted to study the curvature and torsion of slant Frenet curves in 3-dimensional normal almost paracontact metric manifolds. Moreover, in this class of manifolds, properties of non- Frenet slant curves (with null…
We consider the Frenet-Serret geometry of null curves in a three and a four-dimensional Minkowski background. We develop a theory of deformations adapted to the Frenet-Serret frame. We exploit it to provide a Lagrangian description of the…
The aim of this work is to study the Mannheim curves in 3-dimensional Galilean and Pseudo - Galilean space. We obtain the characterizations between the curvatures and torsions of the Mannheim partner curves.
We use the isotropic projection of Laguerre geometry in order to establish a correspondence between plane curves and null curves in the Minkowski $3$-space. We describe the geometry of null curves (Cartan frame, pseudo-arc parameter,…
In this paper, we introduce a new approach to non-lightlike curve pairs by using integral curves in Minkowski 3-space. We consider direction curve and donor curve to study non-lightlike curve couples such as involute-evolute curves,…
In this paper, we give the definition, different types and characterizations of Mannheim partner D-curves in Minkowski 3-space. We find the relations between the geodesic curvatures, the normal curvatures and the geodesic torsions of these…
We discuss some aspects of the differential geometry of curves in Minkowski space. We establish the Serret-Frenet equations in Minkowski space and use them to give a very simple proof of the fundamental theorem of curves in Minkowski space.…
We first prove that, unlike the biharmonic case, there exist triharmonic curves with nonconstant curvature in a suitable Riemannian manifold of arbitrary dimension. We then give the complete classification of triharmonic curves in surfaces…
The aim of this paper is to study the Mannheim partner curves in three dimensional Galilean space . Some well known theorems are obtained related to Mannheim curves.
The aim of this article is to characterize pairs of curves within multiplicative (non-Newtonian) spaces. Specifically, we investigate how famous curve pairs such as Bertrand partner curves, Mannheim partner curves, which are prominent in…
In this paper, the Cartan frames and the equi-affine curvatures are described with the help of the Frenet frames and the Frenet curvatures of a non-null and non-degenerate curve in a 3-dimensional pseudo-Riemannian manifold. The constancy…
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…
In this paper, we study the differential geometry of null Cartan curves under the similarity transformations in the Minkowski space-time. Besides, we extend the fundamental theorem for a null Cartan curve according to a similarity motion.…
In this study, we define a family of null curves in Minkowski 3-space and called null similar curves. We obtain some properties of these special curves. We show that two null curves are null similar curves if and only if these curves form a…