Related papers: Similar Curves With Variable Transformations

In this paper, we define a new type Bertrand curve and this curves are said V-Bertrand curve, f-Bertrand curve and a-Bertrand curve. In addition, we give charectarization of the V-Bertrand curve and we define a Bertrand surface.

We study the geometry of equiclassical strata of the discriminant in the space of plane curves of a given degree, which are families of curves of given degree, genus and class (degree of the dual curve). Our main observation is that the use…

We establish a family of parametric isoperimetric-type inequalities with multiple geometric quantities for closed convex curves. These inequalities hold under certain parameter conditions. We also prove the equality conditions. Some new…

Let $V$ be a finite-dimensional vector space over the finite field ${\mathbb F}_q$ and suppose $W$ and $\widetilde{W}$ are subspaces of $V$. Two linear transformations $T:W\to V$ and $\widetilde{T}:\widetilde{W}\to V$ are said to be similar…

The main subject is the difference between the coarse moduli space and the stack of hyperelliptic curves. In particular, we compute their Picard groups, giving explicit description of the generators. We also study how many families of…

In this note we study curves (arrangements) in the complex projective plane which can be considered as generalizations of free curves. We construct families of arrangements which are nearly free and possess interesting geometric properties.…

Congruence families, i.e., $\ell$-adic convergence for well-defined arithmetic subsequences, is a commonplace phenomenon for the coefficients of modular forms. Such families superficially resemble one another, but they often vary…

This study introduces a new type of general helix called associated helix which is associated to a special surface curve. The basic idea is to determinate the parametric form of an associated helix by means of Darboux frame and surface…

The purpose of this paper is to interpret the phase transition in the Loewner theory as an analog of the hyperbolic variant of the Schur theorem about curves of bounded curvature. We define a family of curves that have a certain conformal…

In this work, first, we express some characterizations of helices and ccr curves in the Euclidean 4-space. Thereafter, relations among Frenet-Serret invariants of Bertrand curve of a helix are presented. Moreover, in the same space, some…

We introduce a special class of real semiflows, which is used to define a general type of evolution semigroups, associated to not necessarily exponentially bounded evolution families. Giving spectral characterizations of the corresponding…

We consider in this paper the $FRS$-deformations of a family of space curves with codimension $\leq 3$. Some geometric aspects of a space curve such as flattenings, vertices and twistings points has been studied.

Inside the symmetric product of a very general curve, we consider the codimension-one subvarieties of symmetric tuples of points imposing exceptional secant conditions on linear series on the curve of fixed degree and dimension. We compute…

In this paper we set up the family Seiberg-Witten theory. It can be applied to the counting of nodal pseudo-holomorphic curves in a symplectic 4-manifold (especially a Kahler surface). A new feature in this theory is that the chamber…

The purpose of this article is to find a family of curves parametrized by arc length and that depend on an angular function and an intrinsic fraction function, which is defined as the quotient between torsion and curvature. We find for this…

We give new examples of plane curves with two or more Galois points as a family, and describe the number of Galois points for these curves, by using finite fields.

Salkowski \cite{salkow}, one century ago, introduced a family of curves with constant curvature but non-constant torsion (Salkowski curves) and a family of curves with constant torsion but non-constant curvature (anti-Salkowski curves) in…

We introduce the concept of deck transformations within the category of developable complexes of groups. Drawing inspiration from classical covering theory for topological spaces, we propose an alternative construction of the universal…

The generic singularities and bifurcations are classified for one-parameter families of curves with frames in a space form, the Euclidean space, the elliptic space or the hyperbolic space via projective geometry. Two kinds of frames are…

We study curves obtained by tracing triangle centers within special families of triangles, focusing on centers and families that yield (semi-)invariant triangle curves, meaning that varying the initial triangle changes the loci only by an…