Related papers: Similar Curves With Variable Transformations
Let X be a (possibly nodal) K-trivial threefold moving in a fixed ambient space P. Suppose X contains a continuous family of curves, all of whose members satisfy certain unobstructedness conditions in P. A formula is given for computing the…
Graph manifolds form important classes of $3$-dimensional closed and orientable manifolds. For example, {\it Seifert} manifolds are graph manifolds where hyperbolic manifolds are not. In applying singularity theory of differentiable maps to…
We make the first attempt to define S-transformations for CFT$_2$ as linear mappings from closed to open sector linear spaces. The definition is based on closed-open sector linear space isomorphisms and boundary condition completeness.…
The orthogonal trajectories of the first tangents of the curve are called the involutes of $x$. The hyperspheres which have higher order contact with a curve $x$ are known osculating hyperspheres of $x$. The centers of osculating…
In this work, notion of a slant helix is extended to space E$^n$. Necessary and sufficient conditions to be a slant helix in the Euclidean $n-$space are presented. Moreover, we express some integral characterizations of such curves in terms…
In this article, circular arcs are considered both individually and as elements of a piecewise circular curve. The endpoint parameterization proves to be quite advantageous here. The perspective of symplectic geometry provides new vectorial…
A genus one curve of degree 5 is defined by the 4 x 4 Pfaffians of a 5 x 5 alternating matrix of linear forms on P^4. We describe a general method for investigating the invariant theory of such models. We use it to explain how we found our…
Let $X$ be a projective variety with an action of a reductive group $G$. Each ample $G$-line bundle $L$ on $X$ defines an open subset $X^{\rm ss}(L)$ of semi-stable points. Following Dolgachev and Hu, define a GIT-class as the set of…
We classify all special homogeneous curves. A special homogeneous curve $\mathcal{H}$ consists of connected components of the hyperbolic points in the level set $\{h=1\}$ of a homogeneous polynomial $h$ in two real variables of degree at…
In this paper, we consider a class of plane curves called log-aesthetic curves and their generalization which are used in computer aided geometric design. We consider these curves in the framework of the similarity geometry and characterize…
We provide a description of W_3 transformations in terms of deformations of convex curves in two dimensional Euclidean space. This geometrical interpretation sheds some light on the nature of finite W_3-morphisms. We also comment on how…
We show that there are five types of planar curves such that arrangements of its translates are combinatorially equivalent to an arrangement of lines. These curves can be used to define norms giving constructions with many unit distances…
Metric algebras are metric variants of $\Sigma$-algebras. They are first introduced in the field of universal algebra to deal with algebras equipped with metric structures such as normed vector spaces. Recently a similar notion of…
We shall give a definition of the curvature operator for a family of weighted Bergman spaces $\{\mathcal H_t\}$ associated to a smooth family of smoothly bounded strongly pseudoconvex domains $\{D_t\}$. In order to study the boundary term…
We define formal orbifolds over an algebraically closed field of arbitrary characteristic as curves together with some branch data. Their \'etale coverings and their fundamental groups are also defined. These fundamental group approximates…
A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any space dimension: we prove that rectifying curves are…
In the previous works, the rational function semifields of abstract tropical curves were characterized. In this paper, we give a contravariant categorical equivalence between the category of abstract tropical curves with morphisms and the…
The theory of voltage graphs has become a standard tool in the study graphs admitting a semiregular group of automorphisms. We introduce the notion of a cyclic generalised voltage graph to extend the scope of this theory to graphs admitting…
In this note, we show that to each elliptic curve of the form $$y^2-axy-y=x^3-bx^2-cx,$$ we can associate a family of lattice paths whose step set is determined by the parameters of the elliptic curve. The enumeration of these lattice paths…
In classical differential geometry, the problem of the determination of the position vector of an arbitrary space curve according to the intrinsic equations $\kappa=\kappa(s)$ and $\tau=\tau(s)$ (where $\kappa$ and $\tau$ are the curvature…