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This note is an attempt to relate explicitly the geometric and algebraic properties of a space curve that is contained in some double plane. We show in particular that the minimal generators of the homogeneous ideal of such a curve can be…
In this paper we investigate the mapping properties in Lebesgue-type spaces of certain generalized Radon transforms defined by integration over curves.
We study the geometry of super curves with a chosen supervolume form. We consider the algebra of divergence free vector fields $S(1|N)$ associated to such curves. When $N=2$ its derived algebra, called $S(2)$, defines a special family of…
In this paper, we derive new shape descriptors based on a directional characterization. The main idea is to study the behavior of the shape neighborhood under family of transformations. We obtain a description invariant with respect to…
Characterizations of all continuous, additive and $\mathrm{GL}(n)$-equivariant endomorphisms of the space of convex functions on a Euclidean space $\mathbb{R}^n$, of the subspace of convex functions that are finite in a neighborhood of the…
A one-dimensional space curve in $\mathbb{R}^{3}$ is a useful nonlinear medium for modeling vortex filaments and biological soft-matter capable of supporting a variety of wave motions. The Hasimoto transformation defines a mapping between…
We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that…
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…
A way to characterize the space of leaves of a foliation in terms of connections is proposed. A particular example of vertex algebra cohomology of codimension one foliations on complex curves is considered.
The deltoid curve in R 2 is the boundary of a domain on which there exist probability measures and orthogonal polynomials for theses measures which are eigenvec-tors of diffusion operators. As such, they may be considered as a two…
Finding appropriate notions of discrete holomorphic maps and, more generally, conformal immersions of discrete Riemann surfaces into 3-space is an important problem of discrete differential geometry and computer visualization. We propose an…
In this study, inextensible flows of curves in four-dimensional pseudo-Galilean space are expressed, and the necessary and sufficient conditions of these curve flows are given as partial differential equations. Also, the directional…
This article describes the mean curvature flow, some of the discoveries that have been made about it, and some unresolved questions.
The purpose of the present paper is to present the main applications of a new method for the determination of the fractal structure of plane curves. It is focused on the inverse problem, that is, given a curve in the plane, find its fractal…
In this paper we explore the geometric structures associated with curvature radii of curves with values on a Riemannian manifold $(M, g)$. We show the existence of sub-Riemannian manifolds naturally associated with the curvature radii and…
An interesting question about the perturbed sequences is: when do they inherit the properties of the original one? An elegant relation between frames (fusion frames) and their perturbations is the relation of their redundancies. In this…
The aim of this paper is to present a new perspective on the generation of developable trajectory ruled surfaces in Minkowski 3-space. Involute trajectory ruled surfaces generated by the Frenet trihedron, moving along spacelike involutes of…
This paper concerns (Lorentz-)Darboux transformations in the Lorentz-Minkowski plane $\mathbb{R}^{1,1}$. We use the Penrose diagram for conformal compactification and show some unique properties of Darboux transformations of spacelike…
In this paper, we have first given easily the characterization of special curves with the help of the Rotation minimizing frame (RMF). Also, rectifying-type curves are generalized n-dimensional space $R_{n}$.
Isophote comprises a locus of the surface points whose normal vectors make a constant angle with a fixed vector. In this paper, isophote curves are studied on timelike surfaces in Minkowski 3-space E31. The axises of spacelike and timelike…