相关论文: New special curves and their spherical indicatrice…

We define a new kind of helicoidal surface of value m. A rotational surface which is isometric to the helicoidal surface of value m is revealed. In addition, we calculate some differential geometric properties of the helicoidal surface 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…

The history of the isoptic curves goes back to the 19th century, but nowadays the topic is experiencing a renaissance, providing numerous new results and new applications. First, we define the notion of isoptic curve and outline some of the…

On a special line bundle $L$ on a projective curve $C$ we introduce a geometric condition called $(\Delta_q)$. When $L=K_C$ this condition implies gon$(C) \ge q+2$. For an arbitrary special $L$ we show that $(\Delta_3)$ implies that $L$ has…

The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…

We define a new geometric flow, which we shall call the $K$-flow, on 3-dimensional Riemannian manifolds; and study the behavior of Thurston's model geometries under this flow both analytically and numerically. As an example, we show that an…

In this study, we define some new types of non-null ruled surfaces called slant ruled surfaces in the Minkowski 3-space E_1^3. We introduce some characterizations for a non-null ruled surface to be a slant ruled surface in E_1^3. Moreover,…

We describe the natural geometry of Hilbert schemes of curves in ${\mathbb P}^3$ and, in some cases, in ${\mathbb P}^n$ , $n\geq 4$.

In this study, we determine some special Smarandache curves in E1 3.We give some characterizations consequences of Smarandache curves.

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…

The writhe of a space curve fragment is considered for various boundary conditions. An expression for the writhe as a function of arclength for an arbitrary space curve is obtained. The formula is built on the base of closing the tangent…

In this paper, we study relatively normal-slant helices lying on timelike as well as spacelike surfaces in Minkowski $3$-space $ \mathbb{E}_1^3$. The axes of spacelike and timelike relatively normal-slant helices are obtained via their…

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 first prove that, unlike the biharmonic case, there exist triharmonic curves with nonconstant curvature in a suitable Riemannian manifold of arbitrary dimension. We then give the complete classification of triharmonic curves in surfaces…

A focal representation of a generic regular curve {\gamma} in E^{m+1} consists of the centers of the osculating hyperplanes. A k-slant helix {\gamma} in E^{m+1} is a (generic) regular curve whose unit normal vector V_{k} makes a constant…

The main motivation of this paper arises from the study of Carnot-Carath\'eodory spaces, where the class of 1-rectifiable sets does not contain smooth non-horizontal curves; therefore a new definition of rectifiable sets including…

A space curve in a Euclidean 3-space $\mathbb E^3$ is called a rectifying curve if its position vector field always lies in its rectifying plane. This notion of rectifying curves was introduced by the author in [Amer. Math. Monthly {\bf…

We develop an essentially algebraic method to study biharmonic curves into an implicit surface. Although our method is rather general, it is especially suitable to study curves into surfaces defined by a polynomial equation: in particular,…

In this paper, we investigate special Smarandache curves according to Bishop frame in Euclidean 3-space and we give some differential geometric properties of Smarandache curves. Also we find the centers of the osculating spheres and…

In this note we extend the theory of twists of elliptic curves as presented in various standard texts for characteristic not equal to two or three to the remaining characteristics. For this, we make explicit use of the correspondence…