Related papers: Associated Curves in $E^3$ from a Different Point …

The {\em focal curve} of an immersed smooth curve $\gamma:s\mapsto \gamma(s)$, in Euclidean space $\R^{m+1}$, consists of the centres of its osculating hyperspheres. The focal curve may be parametrised in terms of the Frenet frame of…

A novel family of integrable third order maps is presented. Each map possesses, by construction, a pair of rational invariants and a commuting map from the same class. The 3-dimensional invariant curve is parametrized, in general, by an…

To any metric spaces there is an associated metric profile. The rectifiability of the metric profile gives a good notion of curvature of a sub-Riemannian space. We shall say that a curvature class is the rectifiability class of the metric…

We construct a tangent bundle exponential map and locally autoparallel coordinates for geometries based on a general connection on the tangent bundle of a manifold. As concrete application we use these new coordinates for Finslerian…

We classify the biharmonic non-Legendre curves in a Sasakian space form for which the angle between the tangent vector field and the characteristic vector field is constant and obtain explicit examples of such curves in…

In this study, the new characterizations of special curves are investigated without using the curvatures of these special curves: general helices, slant helices, Bertrand curves, Mannheim curves. The curvatures are given by the help of the…

Consider a smooth projective curve and a given embedding into projective space via a sufficiently positive line bundle. We can form the secant variety of $k$-planes through the curve. These are singular varieties, with each secant variety…

In this paper we relate some classical normal forms for complex elliptic curves in terms of 4-point sets in the Riemann sphere. Our main result is an alternative proof that every elliptic curve is isomorphic as a Riemann surface to one in…

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…

We construct 9-parameter and 13-parameter dynamical systems of the plane which map bi-quadratic curves to other bi-quadratic curves and return to the original curve after two iterations. These generalize the QRT maps which map each such…

We consider a unit speed curve $\alpha$ in Euclidean four-dimensional space $E^4$ and denote the Frenet frame by $\{T,N,B_1,B_2\}$. We say that $\alpha$ is a slant helix if its principal normal vector $N$ makes a constant angle with a fixed…

This article defines a new family of curves in space, whose graphs generate shapes similar to whirls. An intrinsic equation is found, in terms of curvature and torsion, which gives necessary and sufficient conditions for the existence of…

Let M be a simply connected Riemannian symmetric space, with at most one flat direction. We show that every Riemannian (or unitary) vector bundle with parallel curvature over M is an associated vector bundle of a canonical principal bundle,…

Topological invariants such as winding numbers and linking numbers appear as charges of topological solitons in diverse nonlinear physical systems described by a unit vector field defined on two and three dimensional manifolds. While the…

We consider a family of axisymmetric curves evolving by its mean curvature with driving force in the half space. We impose a boundary condition that the curves are perpendicular to the boundary for $t>0$, however, the initial curve…

We apply classical invariant theory of binary forms to explicitly characterize isomorphism classes of hyperelliptic curves of small genus and, conversely, propose algorithms for reconstructing hyperelliptic models from given invariants. We…

We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense.…

A family of plane oriented continuous paths depending on a fixed real positive number $R$ is considered. For any point $x$ on the path, the previous points lie out of any circle of radius $R$ having at $x$ interior normal in a suitable…

We consider curves which go around Whitney umbrella. Then we consider the geodesic and the normal curvatures, ruled surfaces generated by the normal vector and normal developable surfaces with respect to the tangent and bi-tangent vectors…

We show how the theory of tangles is equivalent to that of well-connected tangles. These are drawn on a surface with boundary, and equivalent via Reidemeister moves of a restricted kind. This reworking of the graphical foundations for link…