Related papers: Some characterizations for the involute curves in …
In this paper, we study Mannheim surface offsets in dual space. By the aid of the E. Study Mapping, we consider ruled surfaces as dual unit spherical curves and define the Mannheim offsets of the ruled surfaces by means of dual geodesic…
We propose a notion of discrete elastic and area-constrained elastic curves in 2-dimensional space forms. Our definition extends the well-known discrete Euclidean curvature equation to space forms and reflects various geometric properties…
We give a sharp lower bound on the area of the domain enclosed by an embedded curve lying on a two-dimensional sphere, provided that geodesic curvature of this curve is bounded from below. Furthermore, we prove some dual inequalities for…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
In this paper we study the general affine geometry of curves in affine space $A^2$. For a regular plane curves we define two kinds of moving frames. The first is of minimal order in all moving frames.The second is the Frenet moving frame.…
In this paper we deal with curves with degeneration degree two in pseudo-Euclidean spaces of index two. We characterize Bertrand curves. We show a correspondence between the evolute of a null curve and the involute of a certain spacelike…
In the present paper, we investigate special Smarandache curves with Darboux apparatus with respect to Frenet and Darboux frame of an arbitrary curve on a surface in the three-dimensional Galilean space G3. Furthermore, we give general…
We investigate the existence of coordinate transformations which bring a given vector field on a manifold equipped with an involutive distribution into the form of a second-order differential equation field with parameters. We define…
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 investigate the position vector of a curve on the surface in the Galilean 3-space G^3. Firstly, the position vector of a curve with respect to the Darboux frame is determined. Secondly, we obtain the standard…
In this paper, we give a approximation characterization, embedding properties and the duality of matrix weighted modulation spaces.
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…
Isophote comprises a locus of the surface points whose normal vectors make a constant angle with a fixed vector. Main objective of this paper is to find the axis of an isophote curve via its Darboux frame and afterwards to give some…
A space curve is determined by conformal arc-length, conformal curvature, and conformal torsion, up to M\"obius transformations. We use the spaces of osculating circles and spheres to give a conformally defined moving frame of a curve in…
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.…
We define four different kinds of multiplicity of an invariant algebraic curve for a given polynomial vector field and investigate their relationships. After taking a closer look at the singularities and at the line of infinity, we improve…
In this study, after introducing algebraic properties of real quaternions some characterizations of quaternionic involute-evolute curves in Q are obtained. And some results and theorems for quaternionic w-curves are given. Lastly, we…
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 slant helix (or $\overset{\_}{\xi}_{2}$-helix) and Darboux helix in Myller configuration $M$. We show that a curve in $M$ is a slant helix if and only if it is a Darboux helix. We give the alternative frame of a…
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…