Related papers: Constant Angle Ruled Surfaces in Euclidean Spaces

We solve the problem of finding a sharp upper bound on the minimum angle formed by $N$ points in the Euclidean and Hyperbolic planes.

In this paper, we prove a similar result to the fundamental theorem of regular surfaces in classical differential geometry, which extends the classical theorem to the entire class of singular surfaces in Euclidean 3-space known as frontals.…

We study compact stable embedded minimal surfaces whose boundary is given by two collections of closed smooth Jordan curves in close planes of Euclidean 3-space. Our main result is a classification of these minimal surfaces, under certain…

It is still an open question whether a compact embedded hypersurface in the Euclidean space R^{n+1} with constant mean curvature and spherical boundary is necessarily a hyperplanar ball or a spherical cap, even in the simplest case of…

In this paper we study surfaces in Euclidean 3-space foliated by pieces of circles and that satisfy a Weingarten condition of type $a H+b K=c$, where $a,b$ and $c$ are constant and $H$ and $K$ denote the mean curvature and the Gauss…

Meridian surfaces in the Euclidean 4-space are two-dimensional surfaces which are one-parameter systems of meridians of a standard rotational hypersurface. On the base of our invariant theory of surfaces we study meridian surfaces with…

Weingarten surfaces are those whose principal curvatures satisfy a functional relation, whose set of solutions is called the curvature diagram or the W-diagram of the surface. Making use of the notion of geometric linear momentum of a plane…

We characterize all ruled translating solitons in Minkowski 3-space. In contrast to the Euclidean space, we find ruled translating solitons that are not cylindrical. These surfaces appear when the vector field that defines the rulings,…

In this paper we consider the spherical slant helices in $R^3$. More- over, we show how could be obtained to a spherical slant helix and we give some spherical slant helix examples in Euclidean 3-space.

A class of surfaces-graphs in a Riemannian 3-space with a prescribed projection of one field of principal directions onto a surface $\Pi$ is considered. A problem of determination of such surfaces when both principal curvatures are given…

In this paper, we consider the mean curvature flow of convex hypersurfaces in Euclidean spaces with a general forcing term. We show that the flow may shrink to a point in finite time if the forcing term is small, or exist for all times and…

The conic sections, as well as the solids obtained by revolving these curves, and many of their surprising properties, were already studied by Greek mathematicians since at least the fourth century B.C. Some of these properties come to the…

Surface geometry plays a central role in the design of bridges, vaults and shells, using various techniques for generating a geometry which aims to balance structural, spatial, aesthetic and construction requirements. In this paper we…

In this work, we study some classes of rotational surfaces in the pseudo-Euclidean space $\mathbb{E}^4_t$ with profile curves lying in 2-dimensional planes. First, we determine all such surfaces in the Minkowski 4-space $\mathbb{E}^4_1$…

We classify all ruled surfaces in Euclidean space that are critical points of the Dirichlet energy, obtaining explicit parametrizations of these surfaces.

We establish uniqueness and regularity results for tangent cones (at a point or at infinity) with isolated singularities arising from a given immersed stable minimal hypersurface with suitably small (non-immersed) singular set. In…

In the present paper we consider a special class of Lorentz surfaces in the four-dimensional pseudo-Euclidean space with neutral metric which are one-parameter systems of meridians of rotational hypersurfaces with timelike or spacelike axis…

In this work we present a study on the characterization of ordered and disordered hyperuniform point distributions on spherical surfaces. In spite of the extensive literature on disordered hyperuniform systems in Euclidean geometries, to…

This work investigates slant timelike-ruled surfaces and their evolute offsets in Minkowski 3-space $\mathbb{E}_{1}^{3}$. Using the symmetry of evolute curves, we derive a parametric formulation for skew timelike-ruled surfaces and…

In this paper, we consider non developable ruled surface with spacelike ruling, timelike ruling, respectively. We give the relations between the structure functions with the curvature and torsion of the striction line of the timelike and…