Related papers: Triple-Point Defective Ruled Surfaces
In this paper we study the linear series |L-3p| of hyperplane sections with a triple point p of a surface S embedded via a very ample line bundle L for a general point p. If this linear series does not have the expected dimension we call…
In this paper we study the linear series $|L-3p|$ of hyperplane sections with a triple point $p$ on a surface $S$ embedded via a very ample line bundle $L$ for a \emph{general} point $p$. If this linear series does not have the expected…
We study linear systems of surfaces in $\mathbb{P}^3$ singular along general lines. Our purpose is to identify and classify special systems of such surfaces, i.e., those nonempty systems where the conditions imposed by the multiple lines…
In this paper we prove a conjecture about the dimension of linear systems of surfaces of degree d in P^3 through at most eight multiple points in general position.
In this study, we define some new types of ruled surfaces called slant ruled surfaces. We give some characterizations for a regular ruled surface to be a slant ruled surface in Euclidean 3- space. We show that if the slant ruled surface is…
In this paper we compute upper bounds for the number of ordinary triple points on a hypersurface in $P^3$ and give a complete classification for degree six (degree four or less is trivial, and five is elementary). But the real purpose is to…
In this paper, we define a new type of ruled surface called ruled surface by using the alternative frame of a base curve. Then, we study its differential geometric properties such as striction line, distribution parameter, fundamental…
We present an algorithm that covers any given rational ruled surface with two rational parametrizations. In addition, we present an algorithm that transforms any rational surface parametrization into a new rational surface parametrization…
Motivated by a number of recent investigations, we define and investigate the various properties of the ruled surfaces depend on three dimensional Lie groups with a bi-variant metric. We give useful results involving the characterizations…
In this study, we investigate the existence theorems for timelike ruled surfaces in Minkowski 3-space. We obtain a general system and give the existence theorems for a timelike ruled surface according to Gaussian curvature, distribution…
The purpose of this note is to study configurations of lines in projective planes over arbitrary fields having the maximal number of intersection points where three lines meet. We give precise conditions on ground fields F over which such…
We prove that any number of general fat points of any multiplicities impose the expected number of conditions on a linear system on a smooth projective surface, in several cases including primitive linear systems on very general K3 and…
We study special linear systems of surfaces of $\mathbb{P}^3$ interpolating nine points in general position having a quadric as fixed component. By performing degenerations in the blown-up space, we interpret the quadric obstruction in…
In this work, ruled surfaces in 3-dimensional Riemannian manifolds are studied. We determine the expression for the extrinsic and sectional curvature of a parametrized ruled surface, where the former one is shown to be non-positive. We also…
We propose a combinatorial method of proving non-specialty of a linear system of curves with multiple points in general positions. As an application we obtain a classification of special linear systems on P1xP1 for which the multiplicities…
In this article, we consider surfaces in the 3-dimensional Euclidean space E3 without parabolic points which are of finite II-type, that is, they are of finite type, in the sense of B.-Y. Chen, corresponding to the second fundamental form.…
In this study, we define a family of ruled surfaces in the Euclidean 3-space E^3 and called similar ruled surfaces. We obtain some properties of these special surfaces and we show that developable ruled surfaces form a family of similar…
The number of apparent double points of an irreducible projective variety $X$ of dimension $n$ in $\mathbb{P}^{2n+1}$ is the number of secant lines to $X$ passing through a general point of $\mathbb{P}^{2n+1}$. This classical notion dates…
We consider skew ruled surfaces in the three-dimensional Euclidean space and some geometrically distinguished families of curves on them whose normal curvature has a concrete form. The aim of this paper is to find and classify all ruled…
We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.