Related papers: Characterizations of Slant Ruled Surfaces in the E…
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…
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…
In this study, we define the generalized normal ruled surface of a curve in the Euclidean 3-space $E^3$. We study the geometry of such surfaces by calculating the Gaussian and mean curvatures to determine when the surface is flat or minimal…
In this paper, we study the special curves and ruled surfaces on helix hypersurface whose tangent planes make a constant angle with a fixed direction in Euclidean n-space Besides, we observe some special ruled surfaces in and give…
In Euclidean space, we investigate surfaces whose mean curvature $H$ satisfies the equation $H=\alpha\langle N,\mathbf{x}\rangle+\lambda$, where $N$ is the Gauss map, $\mathbf{x}$ is the position vector and $\alpha$ and $\lambda$ are two…
In the present paper, a new type of ruled surfaces called osculating-type (OT)-ruled surface is introduced and studied. First, a new orthonormal frame is defined for OT-ruled surfaces. The Gaussian and the mean curvatures of these surfaces…
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…
We consider 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 surfaces…
In this study, we introduce Darboux slant ruled surfaces in the Euclidean 3-space which is defined by the property that the Darboux vector of orthonormel frame of ruled surface makes a constant angle with a fixed, non-zero direction. We…
This paper deals with relative normalizations of skew ruled surfaces in the Euclidean space $\mathbb{E}^{3}$. In section 2 we investigate some new formulae concerning the Pick invariant, the relative curvature, the relative mean curvature…
We consider the Laplace normal vector field of relatively normalized ruled surfaces with non-vanishing Gaussian curvature in the three-dimensional Euclidean space $\mathbb{R}^{3}$. We determine all ruled surfaces and all relative…
In this paper we classify certain special ruled surfaces in $\R^3$ under the general theorem of characterization of constant angle surfaces. We study the tangent developable and conical surfaces from the point of view the constant angle…
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 paper, we study the spherical indicatrices of W-direction curves in three dimensional Euclidean space which were defined by using the unit Darboux vector field W of a Frenet curve, in [11]. We obtain the Frenet apparatus of these…
We study ruled surfaces in R3 which are obtained from dual spher- ical indicatrix curves of dual Frenet vector fields. We find the Gaussian and mean curvatures of the ruled surfaces and give some results of being Wein- garten surface.
We study surfaces with a constant ratio of principal curvatures in Euclidean and simply isotropic geometries and characterize rotational, channel, ruled, helical, and translational surfaces of this kind under some technical restrictions…
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 investigate ruled surfaces in 3d Riemannian manifolds, i.e., surfaces foliated by geodesics. In 3d space forms, we find the striction curve, distribution parameter, and the first and second fundamental forms, from which we obtain the…
We investigate the relationship among characteristic curves on developable surfaces. In case parameter curves coincide with these curves, we show that the base curve of a developable surface could be either a plane curve, a circular helix,…
We consider relative normalizations of ruled surfaces with non-vanishing Gaussian curvature $K$ in the Euclidean space $\mathbb{R} ^{3}$, which are characterized by the support functions $^{\left( \alpha \right) }q=\left \vert K\right \vert…