Related papers: Constant Angle Surfaces in Product Spaces

We suggest a concept of generalized `angles' in arbitrary real normed vector spaces. We give for each real number a definition of an `angle' by means of the shape of the unit ball. They all yield the well known Euclidean angle in the…

The Clifford tori in the 3-sphere are a one-parameter family of flat, two-dimensional, constant mean curvature (CMC) surfaces. This paper demonstrates that new, topologically non-trivial CMC surfaces resembling a pair of neighbouring…

We classify the homogeneous and isoparametric hypersurfaces of $\mathbb{S}^2\times\mathbb{S}^2$. In the classification, besides the hypersurfaces $\mathbb{S}^1(r)\times\mathbb{S}^2,\,r\in (0,1]$, it appears a family of hypersurfaces with…

We investigate the formation of trapped surfaces in cosmological spacetimes, using constant mean curvature slicing. Quantitative criteria for the formation of trapped surfaces demonstrate that cosmological regions enclosed by trapped…

We study in this paper the cluster category C(S,M) of a marked surface (S,M). We explicitly describe the objects in C(S,M) as direct sums of homotopy classes of curves in (S,M) and one-parameter families related to closed curves in (S,M).…

In this paper, we prove a general halfspace theorem for constant mean curvature surfaces. Under certain hypotheses, we prove that, in an ambient space M^3, any constant mean curvature H_0 surface on one side of a constant mean curvature H_0…

We apply the complex analysis over the double numbers $D$ to study the minimal time-like surfaces in $R^4_2$. A minimal time-like surface which is free of degenerate points is said to be of general type. We divide the minimal time-like…

A surface in homogenous space Sol is said to be an invariant surface if it is invariant under some of the two 1-parameter groups of isometries of the ambient space whose fix point sets are totally geodesic surfaces. In this work we study…

At any point of a surface in the four-dimensional Euclidean space we consider the geometric configuration consisting of two figures: the tangent indicatrix, which is a conic in the tangent plane, and the normal curvature ellipse. We show…

We classify the hypersurfaces of dimension n >= 3 with constant sectional curvature in the product spaces R^k x S^{n-k+1} and R^k x H^{n-k+1}, for 2 <= k <= n-1. Our results provide a complete description of these hypersurfaces and extend…

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…

Uniqueness and non-existence results on complete constant mean curvature spacelike hypersurfaces lying between two spacelike slice in the Einstein-de Sitter spacetime are given. They are obtained from a Liouvielle-type theorem applied to a…

For constant mean curvature surfaces of class $C^2$ immersed inside Sasakian sub-Riemannian 3-manifolds we obtain a formula for the second derivative of the area which involves horizontal analytical terms, the Webster scalar curvature of…

Suppose that the surfaces K0 and Kr are the boundaries of two convex, complete, connected C^2 bodies in R^3. Assume further that the (Euclidean) distance between any point x in Kr and K0 is always r (r > 0). For x in Kr, let {\Pi}(x) denote…

Square-tiled surfaces can be classified by their number of squares and their cylinder diagrams (also called realizable separatrix diagrams). For the case of $n$ squares and two cone points with angle $4 \pi$ each, we set up and parametrize…

In this paper, we characterize and classify all surfaces endowed with canonical principal direction relative to a space-like and light-like, constant direction in Minkowski 3-spaces.

In this paper we develop the theory of properly immersed minimal surfaces in the quotient space $\mathbb H^2\times\mathbb R/G,$ where $G$ is a subgroup of isometries generated by a vertical translation and a horizontal isometry in $\mathbb…

In this paper, we study biharmonic hypersurfaces in a product of an Einstein space and a real line. We prove that a biharmonic hypersurface with constant mean curvature in such a product is either minimal or a vertical cylinder generalizing…

In this study, we deal with the local structure of curves and surfaces immersed in a pseudo-isotropic space I_{p}^{3} that is a particular Cayley-Klein space. We provide the formulas of curvature, torsion and Frenet trihedron in order for…

In this paper we define and construct a new class of algebraic surfaces in three-dimensional Euclidean space generated by a curve and a congruence of circles. We study their properties and visualize them with the program Mathematica.