Related papers: Complete biconservative surfaces in $\mathbb{R}^3$…
Surfaces of finite geometric type are complete, immersed into the tree-dimensional Euclidean space with finite total curvature and Gauss map extending to an oriented compact surface as a smooth branched covering map over the unit sphere of…
We construct for every connected surface $S$ of finite negative Euler characteristic and every $H \in [0,1)$, a hyperbolic 3-manifold $N(S,H)$ of finite volume and a proper, two-sided, totally umbilic embedding $f\colon S\to N(S,H)$ with…
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…
We prove that for any open Riemann surface $M$ and any non constant harmonic function $h:M \to \mathbb{R},$ there exists a complete conformal minimal immersion $X:M \to \mathbb{R}^3$ whose third coordinate function coincides with $h.$ As a…
We consider the problem of when a closed hyperbolic surface admits a totally geodesic embedding into a closed hyperbolic 3-manifold, and in particular equivariant versions of such embeddings. In a previous paper we considered…
In this paper are studied the nets of principal curvature lines on surfaces embedded in Euclidean $3-$space near their end points, at which the surfaces tend to infinity. This is a natural complement and extension to smooth surfaces of the…
We obtain sharp estimates involving the mean curvatures of higher order of a complete bounded hypersurface immersed in a complete Riemannian manifold. Similar results are also given for complete spacelike hypersurfaces in Lorentzian ambient…
We study surfaces with one constant principal curvature in Riemannian and Lorentzian three-dimensional space forms. Away from umbilic points they are characterized as one-parameter foliations by curves of constant curvature, each of these…
In this paper we study biconservative hypersurfaces $M$ in space forms $\overline M^{n+1}(c)$ with four distinct principal curvatures whose second fundamental form has constant norm. We prove that every such hypersurface has constant mean…
We provide a classification of compact Euclidean submanifolds $M^n\subset{\mathbb{R}}^{n+2}$ with nonnegative sectional curvature, for $n\ge 3$. The classification is in terms of the induced metric (including the diffeomorphism…
We obtain an estimate for the norm of the second fundamental form of stable H-surfaces in Riemannian 3-manifolds with bounded sectional curvature. Our estimate depends on the distance to the boundary of the surface and on the bounds on the…
Minimal surfaces in the Riemannian product of surfaces of constant curvature have been considered recently, particularly as these products arise as spaces of oriented geodesics of 3-dimensional space-forms. This papers considers more…
In this paper, we study harmonic Riemannian submersions from 3-dimensional geometries using the ( generalized) integrability data associated to an orthonormal frame natural to a Riemannian submersion. We give complete classifications of…
In this work, we are interested in the differential geometry of surfaces in simply isotropic $\mathbb{I}^3$ and pseudo-isotropic $\mathbb{I}_{\mathrm{p}}^3$ spaces, which consists of the study of $\mathbb{R}^3$ equipped with a degenerate…
In this paper we show that a complete and non-compact surface immersed in the Euclidean space with quadratic extrinsic area growth has finite total curvature provided the surface has tamed second fundamental form and admits total curvature.…
In this article we fully classify regular tubular surfaces in Euclidean, Lorentzian and hyperbolic 3-spaces whose Gaussian and mean curvatures $K$ and $H$ verify a polynomial relation. More precisely, we determine the set $S(Q)$ of all…
We investigate isometric immersions $f\colon M^n\to\R^{n+2}$, $n\geq 3$, of Riemannian manifolds into Euclidean space with codimension two that admit isometric deformations that preserve the metric of the Gauss map. In precise terms, the…
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 paper, we study biconservative submanifolds in $\mathbb{S}^{n}\times \mathbb{R}$ and $\mathbb{H}^{n}\times \mathbb{R}$ with parallel mean curvature vector field and co-dimension 2. We obtain some necessary and sufficient conditions…
In this paper, we investigate the geometry of compact spacelike biconservative hypersurfaces with constant scalar curvature in de Sitter space $\mathbb{S}_1^{m+1}(c)$, under some geometric constraints. Our results extend the understanding…