Related papers: Ribaucour-type surfaces

In this work we generalize the surfaces studied in [8], we define the generalization of Ribaucour-type surfaces (in short, GRT-surfaces). We obtain present a representation for GRT-surfaces with prescribed Gauss map which depends on two…

We introduce a class of surfaces in euclidean space motivated by a problem posed by \'{E}lie Cartan. This class furnishes what seems to be the first examples of pairs of non-congruent surfaces in euclidean space such that, under a…

Superconformal surfaces in Euclidean space are the ones for which the ellipse of curvature at any point is a nondegenerate circle. They can be characterized as the surfaces for which a well-known pointwise inequality relating the intrinsic…

In the work \cite{Laredo} the author shows that every hypersurface in Euclidean space is locally associated to the unit sphere by a sphere congruence, whose radius function $R$ is a geometric invariant of hypersurface. In this paper we…

A geometric construction is provided that associates to a given flat front in $\mathbb{H}^3$ a pair of minimal surfaces in $\mathbb{R}^3$ which are related by a Ribaucour transformation. This construction is generalized associating to a…

In this work we define the surfaces spherical type via support function (in short, SS-surfaces). We present a Weierstrass type representation for SS-surfaces with prescribed Gauss map which depends on two holomorphic functions. Also, we use…

We classify all rotational surfaces in Euclidean space whose principal curvatures $\kappa_1$ and $\kappa_2$ satisfy the linear relation $\kappa_1=a\kappa_2+b$, where $a$ and $b$ are two constants. We give a variational characterization of…

An explicit construction of surfaces with flat normal bundle in the Euclidean space (unit hypersphere) in terms of solutions of certain linear system is proposed. In the case of 3-space our formulae can be viewed as the direct Lie sphere…

While a generic smooth Ribaucour sphere congruence admits exactly two envelopes, a discrete R-congruence gives rise to a 2-parameter family of discrete enveloping surfaces. The main purpose of this paper is to gain geometric insights into…

A stationary rotating surface is a compact surface in Euclidean space whose mean curvature $H$ at each point $x$ satisfies $2H(x)=a r^2+b$, where $r$ is the distance from $x$ to a fixed straight-line $L$, and $a$ and $b$ are constants.…

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…

We discuss channel surfaces in the context of Lie sphere geometry and characterise them as certain $\Omega_{0}$-surfaces. Since $\Omega_{0}$-surfaces possess a rich transformation theory, we study the behaviour of channel surfaces under…

In this work we study surfaces in radial conformally flat spaces. We characterize surfaces of rotation with constant Gaussian and Extrinsic curvature in these radial 3-spaces. We prove that all the spheres in the conformal 3-space have…

We study rotational surfaces in Euclidean 3-space whose Gauss curvature is given as a prescribed function of its Gauss map. By means of a phase plane analysis and under mild assumptions on the prescribed function, we generalize the…

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 $\mathbb{E}^4_1$…

In this article we introduce the notion of a Ribaucour partial tube and use it to derive several applications. These are based on a characterization of Ribaucour partial tubes as the immersions of a product of two manifolds into a space…

We classify rotational surfaces in the three-dimensional Euclidean space whose Gaussian curvature $K$ satisfies \begin{equation*} K\Delta K - \|\nabla K\|^2-4K^3 = 0. \end{equation*} These surfaces are referred to as rotational Ricci…

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 consider Lie minimal surfaces, the critical points of the simplest Lie sphere invariant energy, in Riemannian space forms. These surfaces can be characterized via their Euler-Lagrange equations, which take the form of differential…

We apply the invariant theory of surfaces in the four-dimensional Euclidean space to the class of general rotational surfaces with meridians lying in two-dimensional planes. We find all minimal super-conformal surfaces of this class.