Related papers: Linear Weingarten surfaces foliated by circles in …
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…
In this work, we consider spacelike surfaces in Minkowski space $\hbox{\bf E}%_{1}^{3}$ that satisfy a linear Weingarten condition of type $\kappa_{1}=m\kappa_{2}+n$, where $m$ and $n$ are constant and $\kappa_{1}$ and $\kappa_{2}$ denote…
In this work, we study spacelike and timelike surfaces of revolution in Minkowski space $\e_{1}^{3}$ that satisfy $aH+bK=c$, where $H$ and $K$ denote the mean curvature and the Gauss curvature of the surface and $a$, $b$ and $c$ are…
The aim of this paper is to present a complete description of all rotational linear Weingarten surface into the Euclidean sphere S3. These surfaces are characterized by a linear relation aH+bK=c, where H and K stand for their mean and…
We study the existence of surfaces with constant or prescribed Gauss curvature in certain Lorentzian spacetimes. We prove in particular that every (non-elementary) 3-dimensional maximal globally hyperbolic spatially compact spacetime with…
In this paper, we study the rotational surfaces in the isotropic 3-space I^3. satisfying Weingarten conditions in terms of the relative curvature K (analogue of the Gaussian curvature) and the isotropic mean curvature H. In particular, we…
In this work we find all helicoidal surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is $0$…
This paper concerns the global theory of properly embedded spacelike surfaces in three-dimensional Minkowski space in relation to their Gaussian curvature. We prove that every regular domain which is not a wedge is uniquely foliated by…
A linear Weingarten surface in Euclidean space ${\bf R}^3$ is a surface whose mean curvature $H$ and Gaussian curvature $K$ satisfy a relation of the form $aH+bK=c$, where $a,b,c\in {\bf R}$. Such a surface is said to be hyperbolic when…
Let $M\subset\mathbb{R}^3$ be a properly embedded, connected, complete surface with boundary a convex planar curve $C$, satisfying an elliptic equation $H=f(H^2-K)$, where $H$ and $K$ are the mean and the Gauss curvature respectively -…
In this paper, we study the timelike tubular Weingarten surfaces in 3-dimensional Minkowski space $IR_1^3 $.We have obtained some conditions for being $({K_{II},H})$, $({K_{II},K})$, timelike tubular Weingarten surfaces where are the second…
In this paper, we deal with the linear Weingarten factorable surfaces in the isotropic 3-space I^{3} satisfying the relation aK+bH=c, where K is the relative curvature and H the isotropic mean curvature, a,b,cR. We obtain a complete…
In this paper we study surfaces foliated by a uniparametric family of circles in the homogeneous space Sol$_3$. We prove that there do not exist such surfaces with zero mean curvature or with zero Gaussian curvature. We extend this study…
In this paper we review some author's results about Weingarten surfaces in Euclidean space $\r^3$ and hyperbolic space $\h^3$. We stress here in the search of examples of linear Weingarten surfaces that satisfy a certain geometric property.…
Spacelike intrinsic rotational surfaces with constant mean curvature in the Lorentz-Minkowski space $\E_1^3$ have been recently investigated by Brander et al., extending the known Smyth's surfaces in Euclidean space. Assuming that the…
Riemann zero mean curvature examples in the Lorentz-Minkowski space are surfaces with zero mean curvature foliated by circles contained in parallel planes. In contrast to the Euclidean case, this family of surfaces presents new and rich…
A zero mean curvature surface in the Lorentz-Minkowski 3-space is said to be of Riemann-type if it is foliated by circles and at most countably many straight lines in parallel planes. We classify all zero mean curvature surfaces of…
We propose a new approach to the study of rotational surfaces in Lorentz-Minkowski space based on the notion of the geometric linear momentum of the generatrix curves with respect to the axes of revolution. This technique allows us to…
In this paper we study surfaces in Euclidean 3-space that satisfy a Weingarten condition of linear type as $\kappa_1=m \kappa_2 +n$, where $m$ and $n$ are real numbers and $\kappa_1$ and $\kappa_2$ denote the principal curvatures at each…
In this paper we solve the Plateau problem for spacelike surfaces with constant mean curvature in Lorentz-Minkowski three-space $\l^3$ and spanning two circular (axially symmetric) contours in parallel planes. We prove that rotational…