Related papers: On a New Type Mannheim Curve

Spherical $t$-designs are finite point sets on the unit sphere that enable exact integration of polynomials of degree at most $t$ via equal-weight quadrature. This concept has recently been extended to spherical $t$-design curves by the use…

Let $E$ be a smooth cubic. A plane curve $D$ is said to be an $n$-contact curve to $E$ if the intersection multiplicities at each intersection point between $E$ and $D$ is $n$. In this note, we give an algorithm to produce $n$-contact…

Let $S$ be a closed orientable hyperbolic surface, and let $\mathcal{O}(K,S)$ denote the number of mapping class group orbits of curves on $S$ with at most $K$ self-intersections. Building on work of Sapir [16], we give upper and lower…

In this paper we produce infinitely many examples of set-theoretic complete intersection monomial curves in $\mathbb{P}^{n+1}$, starting with a set-theoretic complete intersection monomial curve in $\mathbb{P}^{n}$ . In most of the cases…

In this work we present explicit examples of maximal and minimal curves over finite fields in odd characteristic. The curves are of Artin-Schreier type and the construction is closely related to quadratic forms from $\mathbb{F}_{q^n}$ to…

A quadric in $\R P^3$ cuts a curve of degree 6 on a cubic surface in $\R P^3$. The papers classifies the nonsingular curves cut in this way on non-singular cubic surfaces up to homeomorphism. Two issues new in the study related to the first…

We introduce the notion of $k$-type slant helix in Minkowski space $\e_1^4$. For partially null and pseudo null curves in $\e_1^4$, we express some characterizations in terms of their curvature and torsion functions.

In this paper, we survey recent works on the structure of the mapping class groups of surfaces mainly from the point of view of topology. We then discuss several possible directions for future research. These include the relation between…

Let V be a plane smooth cubic curve over a finitely generated field k. The Mordell-Weil theorem for V states that there is a finite subset P \subset V(k) such that the whole V(k) can be obtained from P by drawing secants and tangents…

We present a new technique to study Jacobian variety decompositions using subgroups of the automorphism group of the curve and the corresponding intermediate covers. In particular, this new method allows us to produce many new examples of…

We construct the infinite sequence of invariants for curves in surfaces by using word theory that V. Turaev introduced. For plane closed curves, we add some extra terms, e.g. the rotation number. From these modified invariants, we get the…

We give a classification and a construction of all smooth $(n-1)$-dimensional varieties of lines in ${\bf P}\sp n$ verifying that all their lines meet a curve. This also gives a complete classification of $(n-1)$-scrolls over a curve…

We continue the investigation of curves of type p,q started in [KKW]. We study the space of such curves and the space of nodal curves with prescribed Weierstra\ss semigroup. A necessary and sufficient criterion for a numerical semigroup to…

Properties of the recently reported homogeneous Hilbert curves are deduced and reported. The nature of the affine transformations involved in the construction of the Hilbert curves is explored. The analytical representation of proper and…

These are expanded notes from lectures on the geometry of spherical varieties given in Sanya. We review some aspects of the geometry of spherical varieties. We first describe the structure of $B$-orbits. Using the local structure theorems,…

We consider various equivalence relations on the set of homotopy classes of curves on a hyperbolic surface based on topological, algebraic, and geometric structures. The purpose of this work is to determine the relationship between these…

In this mostly expository paper we review several known results about the cohomology of moduli spaces of smooth and stable curves, focusing in particular on low degree cohomology. We also give a new proof of Harer's theorem describing the…

We show that the topological classification and the smooth classification are generically the same for certain families of plane curves in a semi-local case(the double local case). Especially we give the normal form of transversely jointed…

In this paper, we give a definition of harmonic curvature functions in terms of V_{n} and define a new kind of slant helix which is called V_{n}-slant helix in n-dimensional pseudo-Riemannian manifold. Also, we give important…

Genus 5 curves can be hyperelliptic, trigonal, or non-hyperelliptic non-trigonal, whose model is a complete intersection of three quadrics in $\mathbb{P}^4$. We present and explain algorithms we used to determine, up to isomorphism over…