Related papers: Constant Angle Surfaces in Product Spaces

We prove a vertical halfspace theorem for surfaces with constant mean curvature $H={1/2},$ properly immersed in the product space $\h^2\times\re,$ where $\h^2$ is the hyperbolic plane and $\re$ is the set of real numbers. The proof is a…

Consider the Euclidean space $\mathbb{R}^3$ endowed with a canonical semi-symmetric non-metric connection determined by a vector field $\mathsf{C}\in\mathfrak{X}(\mathbb{R}^3)$. We study surfaces when the sectional curvature with respect to…

We study stable compact constant mean curvature surfaces in the product spaces S2 X R and H2 X R and in some other Riemannian 3-manifolds.

In this paper, based on the theory of surfaces in the four-dimensional Euclidean space which generalizes the theory of surfaces in three-dimensional Euclidean space, beside other results, we will give a characterization of points on…

In this paper we study minimal and constant mean curvature (cmc) periodic surfaces in H^2 x R. More precisely, we consider quotients of H^2 x R by discrete groups of isometries generated by horizontal hyperbolic translations f and/or a…

We explore convex shapes $S$ in the Euclidean plane which have the following property: there is a circle $C$ such that the angle between the two tangents from any point of $C$ to $S$ is constant equal to $\alpha$. A dynamical formulation…

We consider general relativity with cosmological constant minimally coupled to electromagnetic field and assume that four-dimensional space-time manifold is the warped product of two surfaces with Lorentzian and Euclidean signature metrics.…

Given $H\in [0,\infty),$ some sufficient conditions for existence of CMC $H$ graphs with boundary in two parallel planes of $\mathbb{H}^2\times\mathbb{R}$ are presented. Height estimates for outwards-oriented CMC surfaces…

We prove that every complete connected immersed surface with positive extrinsic curvature $K$ in $H^2\times R$ must be properly embedded, homeomorphic to a sphere or a plane and, in the latter case, study the behavior of the end. Then, we…

For $2+1$ spacetime dimensions, we derive sufficient conditions for the twisting function in a twisted product spacetime, such that there is a global foliation by spacelike CMC surfaces.

We consider surfaces with parallel mean curvature vector (pmc surfaces) in $\mathbb{C}P^n\times\mathbb{R}$ and $\mathbb{C}H^n\times\mathbb{R}$, and, more generally, in cosymplectic space forms. We introduce a holomorphic quadratic…

We give a complete classification of umbilical surfaces of arbitrary codimension of a product $Q^{n_1}_{k_1}\times Q^{n_2}_{k_2}$ of space forms whose curvatures satisfy $k_1 + k_2 \not= 0$.

A classification of 2-dimensional surfaces imbedded in spacetime is presented, according to the algebraic properties of their shape tensor. The classification has five levels, and provides among other things a refinement of the concepts of…

In this paper, we classify the hypersurfaces of $\mathbb{S}^2\times\mathbb{S}^2$ with constant sectional curvature. By applying the so-called Tsinghua principle, which was first discovered by the first three authors in 2013 at Tsinghua…

In this paper, we classify the rotational surfaces with constant skew curvature in $3$-space forms. We also give a variational characterization of the profile curves of these surfaces as critical points of a curvature energy involving the…

Consider a surface $M^2$ with Gaussian curvature either $< 0$ or $> 0$. We prove that in $M^2\times \mathbb{R}^n$ cylinders are characterized as the hypersurfaces with both the extrinsic and intrinsic curvatures equal to zero.

In this paper we study rotational surfaces in the space $\mathbb{H}^2\times\mathbb{R}$ whose mean curvature is given as a prescribed function of their angle function. These surfaces generalize, among others, the ones of constant mean…

In this article we consider surfaces in the product space $\h^2\times \r$ of the hyperbolic plane $\h^2$ with the real line. The main results are: a description of some geometric properties of minimal graphs; new examples of complete…

We give a complete description of all hypersurfaces of the product spaces $\Sf^n\times \R$ and $\Hy^n\times \R$ that have flat normal bundle when regarded as submanifolds with codimension two of the underlying flat spaces $\R^{n+2}\supset…

We consider constant mean curvature surfaces of finite topology, properly embedded in three-space in the sense of Alexandrov. Such surfaces with three ends and genus zero were constructed and completely classified by the authors in…