Related papers: Similar Curves With Variable Transformations

In this long survey article we show that the theory of elliptic and hyperelliptic curves can be extended naturally to all superelliptic curves. We focus on automorphism groups, stratification of the moduli space $\mathcal{M}_g$, binary…

We study a specific class of deformations of curve singularities: the case when the singular point splits to several ones, such that the total $\delta$ invariant is preserved. These are also known as equi-normalizable or equi-generic…

In this paper, we investigate the similarity transformations in the Minkowski-n space. We study the geometric invariants of non-null curves under the similarity transformations. Besides, we extend the fundamental theorem for a non-null…

In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum…

We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.

We introduce the Frenet theory of curves in dual space $\d^3$. After defining the curvature and the torsion of a curve, we classify all curves in dual plane with constant curvature. We also establish the fundamental theorem of existence in…

Here we consider degenerations of stable spin curves for a fixed smoothing of a non-stable curve: we are able to give enumerative results and a description of limits of stable spin curves. We give a geometrically meaningful definition of…

Here we introduce the concept of special effect curve which permits to study, from a different point of view, special linear systems in P^2, i.e. linear system with general multiple base points whose effective dimension is strictly greater…

We consider the curves whose all normal planes are at the same distance from a fixed point and obtain some characterizations of them in the 3-dimensional Euclidean space.

We give a characterization of the effect of sequences of pivot operations on a graph by relating it to determinants of adjacency matrices. This allows us to deduce that two sequences of pivot operations are equivalent iff they contain the…

Let X be a smooth, complete, toric variety. We study those curves C in X that are contractible, in the sense that there exists an equivariant morphism with connected fibers, with source X, that contracts exactly the irreducible curves that…

A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.

This study defines finite-type invariants for curves on surfaces and reveals the construction of these finite-type invariants for stable homeomorphism classes of curves on compact oriented surfaces without boundaries. These invariants are a…

We consider the class of curves of finite total curvature, as introduced by Milnor. This is a natural class for variational problems and geometric knot theory, and since it includes both smooth and polygonal curves, its study shows us…

In this paper, we introduce isophote curves on surfaces in Galilean 3-space. Apart from the general concept of isophotes, we split our studies into two cases to get the axis d of isophote curves lying on a surface such that d is an…

The paper is devoted to the description of family of scalene triangles for which the triangle formed by the intersection points of bisectors with opposite sides is isosceles. We call them Sharygin triangles. It turns out that they are…

Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. Method for general construction of star product is presented. Corresponding twist, expressed in terms of phase space…

We find relations between quantities defining geometry and quantities defining the length of a curve in geometries underlying Electromagnetism and unified model of Electromagnetism and Gravitation. We show that the length of a vector…

A complex elliptic curve $E$ can be defined as the quotient of the analytic space $\mathbb{C}^*$ by a discrete action of the cyclic group $q^{\mathbb{Z}}$ for $\vert q\vert \neq 1$. We study the boundary case when $\vert q\vert =1$, which…

In this paper, we introduce the quaternionic similar curves in 4-dimensional Euclidean space. We show that the families of quaternionic curves with vanishing curvatures form the families of quaternionic similar curves.