arXiv research

Paper finds infinite pairs of fiber-type curves with same topology but different embeddings.

We prove similar theorems concerning the structure of bundles involving complements of fiber-type hyperplane arrangements and orbit configuration spaces. These results facilitate analysis of the fundamental groups of these spaces, which may be viewed as generalizations of the Artin pure braid group. In particular, we r…

A deformation of the Orlik-Solomon algebra of a matroid M is defined as a quotient of the free associative algebra over a commutative ring R with 1. It is shown that the given generators form a Groebner basis and that after suitable homogenization the deformation and the Orlik-Solomon have the same Hilbert series as R-…

Using a recent result of Bartels and Lueck (arXiv:0901.0442) we deduce that the Farrell-Jones Fibered Isomorphism conjecture in L-theory is true for any group which contains a finite index strongly poly-free normal subgroup, in particular, for the Artin full braid groups. As a consequence we explicitly compute the surg…

Unified Long-Moody and Katz methods for constructing local systems.

Study of tangent bundle positivity on complex projective varieties.

Poly-free groups are constructed as iterated semidirect products of free groups. The class of poly-free groups includes the classical pure braid groups, fundamental groups of fiber-type hyperplane arrangements, and certain subgroups of the automorphism groups of free groups. The purpose of this article is to compute ce…

The study explores Bertrand and Mannheim curves in 4D Euclidean space for framed curves.

The study examines Bertrand Legendre curves in the unit tangent bundle over Euclidean plane.

Method for generating new curves from plane curves on cylinders.

In this study, we introduce a new approach to curve pairs by using integral curves. We consider the direction curve and donor curve to study curve couples such as involute-evolute curves, Mannheim partner curves and Bertrand partner curves. We obtain new methods to construct partner curves of a unit speed curve and giv…

The paper characterizes curves in pseudo-Galilean 4-space.

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, Mannheim partner curves and Bertrand partner curves. We obtain new methods to construct…

The paper explores Bertrand and framed curves in 3D space.

The paper examines how closed curves on surfaces intersect and how this intersection determines the curves.

Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By certified, we mean that the approximation can approximate the given curve to any given pr…

Flow deforms locally convex curves to curves of constant k-order width.

Modified curve shortening flow constructs $λ$-Angenent curve.

Study on CR curves in 3-sphere, focusing on critical curves integration and existence.

Study rectifying curves in 3D multiplicative Euclidean space.

In classical curve theory, the geometry of a curve in three dimensions is essentially characterized by their invariants, curvature and torsion. When they are given, the problem of finding a corresponding curve is known as 'solving natural equations'. Explicit solutions are known only for a handful of curve classes, inc…

Unified description of aesthetic curves through self-affinities.

Primitive curves in handlebodies form a connected complex.

Study on Bertrand lightcone framed curves in Lorentz-Minkowski 3-space.

In this study, we introduce a new type of surface curves called D-type curve. This curve is defined by the property that the unit Darboux vector W0 of a space curve r(s) and unit surface normal n along the curve r(s) satisfy the condition <n,W0>=constant. We point out that a D-type curve is a geodesic curve or an asymp…

Study on triharmonic curves in f-Kenmotsu manifolds.

The paper generalizes rectifying and normal curves in Lorentzian n-space.

Compact curve solution emerges from non-compact curve.

New findings on hyperbolicity of fine curve graphs and their subgraphs.

In this paper we study null Bertrand curves in $R_{1}^{4}$ under the assumption the curve has a Cartan frame. We show that if the derivative vectors of the null Cartan curve in $R_{1}^{4}$ is linearly independent, then this curve is not a Bertrand curve. Since then the already known notion of null Bertrand curves in $R…

Homotopy types of curve and arc complexes are studied.

Study of $p$-biharmonic curves and their properties.

In this study, we define a new type of direction curves in the Euclidean 3-space such as osculating-direction curve. We give the characterizations for these curves. Moreover, we obtain the relationships between osculating direction curves and some special curves such as helix, slant helix or rectifying curves.

We classify curves in the moduli space of curves that are both Shimura- and Teichmueller curves: Except for the moduli space of genus one curves there is only a single such curve. We start with a Hodge-theoretic description of Shimura curves and of Teichmueller curves that reveals similarities and differences of the tw…

In this paper we consider the idea of Bertrand curves for curves lying on surfaces and by considering the Darboux frames of them we define these curves as Bertrand D-curves and give the characterizations for these curves. We also find the relations between the geodesic curvatures, the normal curvatures and the geodesic…

The paper studies a curve flow preserving anisotropic length for convex curves, leading to a homothetic limit.

Rectangular peg problem solved for many curves.

Characterizes covers using simple closed curves on surfaces.

We study pairs of curves with Poncelet's porism properties and compute their vertex curves.

In this paper we consider the idea of Mannheim partner curves for curves lying on surfaces and by considering the Darboux frames of them we define these curves as Mannheim partner D-curves and give the characterizations for these curves. We also find the relations between the geodesic curvatures, the normal curvatures …

Defines signed quasiregular curves and proves growth theorem.

In this paper, we consider the idea of Bertrand curves for curves lying on surfaces in Minkowski 3-space. By considering the Darboux frame, we define these curves as Bertrand D-curves and give the characterizations for those curves. We also find the relations between the geodesic curvatures, the normal curvatures and t…

We show that one can define a spectral curve for the Cauchy-Riemann operator on a punctured elliptic curve if one imposes appropriate boundary conditions. Algebraic curves of the type thus obtained appear as irreducible components of spectral curves of minimal tori with planar ends in R^3. It appears that these curves …

In this paper, we give the defination of harmonic curvature function some special curves such as helix, slant curves, Mannheim curves and Bertrand curves. Then, we recall the characterizations of helices [8], slant curves (see [19]) and Mannheim curves (see [12]) in three dimensional Lie groups using their harmonic cur…

In classical curve theory, the geometry of a curve in three dimensions is essentially characterized by their invariants, curvature and torsion. When they are given, the problem of finding a corresponding curve is known as 'solving natural equations'. Explicit solutions are known only for a handful of curve classes, inc…

Using the moving frame and invariants, any discrete curve in $\R^3$ could be uniquely identified by its centroaffine curvatures and torsions. In this paper, depending on the affine curvatures of the fractal curves, such as Koch curve and Hilbert curve, we can clearly describe their iterative regularities. Interestingly…

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 null Bertrand pair. Moreover, we obtain that the family of null geodesics and n…

Study of curves in dual space with constant curvature and torsion.