Related papers: On a new type Bertrand curve
We define a (co-)Poisson (co)algebra of curves on a bordered surface. A bordered surface is a surface whose boundary have marked points. Curves on the bordered surface are oriented loops and oriented arcs whose endpoints in the set of…
We consider a special type of self-similar sets, called fractal squares, and give a brief review on recent results and unsolved issues with an emphasis on their topological properties.
A procedure for interpolating between specified points of a curve or surface is described. The method guarantees slope continuity at all junctions. A surface panel divided into p x q contiguous patches is completely specified by the…
Let $\mathbb{K}$ be an algebraically closed field of characteristic $p>0$. A pressing problem in the theory of algebraic curves is the determination of the $p$-rank of a (nonsingular, projective, irreducible) curve $\mathcal{X}$ over…
We give an upper bound for the degree of rational curves in a family that covers a given birational ruled surface in projective space. The upper bound is stated in terms of the degree, sectional genus and arithmetic genus of the surface. We…
In this paper, we study the computation of curvatures at the singular points of algebraic curves and surfaces. The idea is to convert the problem to compute the curvatures of the corresponding regular parametric curves and surfaces, which…
The fine 1-curve graph of a surface is a graph whose vertices are simple closed curves on the surface and whose edges connect vertices that intersect in at most one point. We show that the automorphism group of the fine 1-curve graph is…
We introduce the notion of tropical curves of hyperelliptic type. These are tropical curves whose Jacobian is isomorphic to that of a hyperelliptic tropical curve, as polarized tropical abelian varieties. We show that this property depends…
In n-dimensional Euclidean space E^n, harmonic curvatures of a non-degenerate curve defined by \"Ozdamar and Hacisaliho\u{g}lu [4]. In this paper, We define a new type of curves called LC helix when the angle between tangent of this curve…
This is a survey describing recents developments in enumerative geometry of curves on projective varieties. Various methods to arrive at results such as Kontsevich's formula for plane rational curves, or Caporaso-Harris's formula for plane…
In this paper we present geometry of some curves in Taxicab metric. All curves of second order and trifocal ellipse in this metric are presented. Area and perimeter of some curves are also defined.
We give a sharp bound on the number of automorphisms of a stable curve of a given genus and describe all curves attaining this bound.
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…
The aim of the paper is to give a method of constructing k-slant curves via any plane curve.
In this research, we introduce an algorithm that produces what appears to be a new mathematical object as a consequence of projecting the \( n \)-dimensional \( Z \)-curve onto an \( n \)-dimensional sphere. The first part presents the…
We define an analogue of the Arnold surface for odd degree flexible curves, and we use it to double branch cover $Q$-flexible embeddings, where $Q$-flexible is a condition to be added to the classical notion of a flexible curve. This allows…
We produce several algebraic curves, some well--known, some new, out of circles, by means of two classical (mutually reciprocal) algebraic methods: blow--down and blow--up.
We study relatively minimal surfaces equipped with a strongly isotrivial elliptic fibration in positive characteristic by means of the notion of equivariantly normal curves introduced and developed recently by Brion. Such surfaces are…
By considering the three dimensional Heisenberg group $\mathbb{H}_1$ as a flat model of pseudo-hermitian manifolds, the authors in [8] derived the Frenet-Serret formulas for curves in $\mathbb{H}_1$. In this notes we show three applications…
We describe our recent work on deformations of hyperelliptic curves by means of integrable hierarchy of hydrodynamic type (nlin.SI/0205012). We also discuss a further extension to the case of non-hyperelliptic curves.