Related papers: Hugelschaffer egg curve and surface

The purpose of this article is to determine explicitly the complete surfaces with parallel mean curvature vector, both in the complex projective plane and the complex hyperbolic plane. The main results are as follows: When the curvature of…

Weingarten surfaces are those whose principal curvatures satisfy a functional relation, whose set of solutions is called the curvature diagram or the W-diagram of the surface. Making use of the notion of geometric linear momentum of a plane…

A simple and efficient algorithm to numerically compute the genus of surfaces of three-dimensional objects using the Euler characteristic formula is presented. The algorithm applies to objects obtained by thresholding a scalar field in a…

A convex triangular grid is represented by a planar digraph $G$ embedded in the plane so that (a) each bounded face is surrounded by three edges and forms an equilateral triangle, and (b) the union $\Rscr$ of bounded faces is a convex…

Let $M^n$ be either a simply connected space form or a rank-one symmetric space of noncompact type. We consider Weingarten hypersurfaces of $M\times\mathbb R$, which are those whose principal curvatures $k_1,\dots ,k_n$ and angle function…

The problem of construction of the surfaces with given sets of the points with horizontal tangential planes is considered. Such considerations are of interest in the problem of computer simulations of the waved ocean surfaces.

An algorithm is given to compute a normal form for hyperelliptic curves. The elliptic case has been treated in a previous paper. In this paper the hyperelliptic case is treated.

We study rational cuspidal curves in Hirzebruch surfaces. We provide two obstructions for the existence of rational cuspidal curves in Hirzebruch surfaces with prescribed types of singular points. The first result comes from Heegaard--Floer…

This tutorial explains how to use piecewise cubic B\'ezier curves to draw arbitrarily oriented ellipses and elliptical arcs. The geometric principles discussed here result in strikingly simple interfaces for graphics functions that can draw…

We prove an existence and uniqueness theorem about spherical helicoidal (in particular, rotational) surfaces with prescribed mean or Gaussian curvature in terms of a continuous function depending on the distance to its axis. As an…

In this paper we define $q$-spherical surfaces as the surfaces that contain the absolute conic of the Euclidean space as a $q-$fold curve. Particular attention is paid to the surfaces with singular points of the highest order. Two classes…

In this study, we consider curves of generalized AW(k)-type of Euclidean n-space. We give curvature conditions of these kind of curves.

Quadratic surfaces gain more and more attention among the Geometric Algebra community and some frameworks were proposed in order to represent, transform, and intersect these quadratic surfaces. As far as the authors know, none of these…

We describe deterministic and probabilistic algorithms to determine whether or not a given monic irreducible polynomial H in Z[X] is a Hilbert class polynomial, and if so, which one. These algorithms can be used to determine whether a given…

There are several examples in which algebraic properties of Jacobian algebras from (unpunctured) Riemann surfaces can be computed from the geometry of the Riemann surface. In this work, we compute the dimension of the Hochschild cohomology…

We investigate helicoidal surfaces in three-dimensional Euclidean space whose profile curves are frontals. Using the framework of Legendre curves and framed surfaces, we establish conditions under which helicoidal surfaces generated by…

We show that the hessian map of quartic plane curves is a birational morphism onto its image, thus bringing new evidence for a very interesting conjecture of Ciro Ciliberto and Giorgio Ottaviani. Our new approach also yields a simpler proof…

Space-filling curves like the Hilbert-curve, Peano-curve and Z-order map natural or real numbers from a two or higher dimensional space to a one dimensional space preserving locality. They have numerous applications like search structures,…

We characterize helix surfaces in the Berger sphere, that is surfaces which form a constant angle with the Hopf vector field. In particular, we show that, locally, a helix surface is determined by a suitable 1-parameter family of isometries…

We prove that a surface carries a hexagonal 3-web of geodesics if and only if the geodesic flow on the surface admits a cubic first integral and show that the system of partial differential equations, governing metrics on such surfaces, is…