Related papers: Characterizing a surface by invariants

We define and study a new numerical invariant of an algebraic group action which we call the canonical dimension. We then apply the resulting theory to the problem of computing the minimal number of parameters required to define a generic…

We use a canonical parametrization of twisted geometries describing the classical phase space of loop quantum gravity on a fixed graph, and establish its explicit correspondence with the associated frame bases and spinorial descriptions.…

We consider the Laplace normal vector field of relatively normalized ruled surfaces with non-vanishing Gaussian curvature in the three-dimensional Euclidean space $\mathbb{R}^{3}$. We determine all ruled surfaces and all relative…

We consider relative normalizations of ruled surfaces with non-vanishing Gaussian curvature $K$ in the Euclidean space $\mathbb{R} ^{3}$, which are characterized by the support functions $^{\left( \alpha \right) }q=\left \vert K\right \vert…

Here, we focus on focal surfaces of a tubular surface in Euclidean 3-space E^3: Firstly, we give the tubular surfaces with respect to Frenet and Darboux frames. Then, we define focal surfaces of these tubular surfaces. We get some results…

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…

Roughly speaking, the problem of geography asks for the existence of varieties of general type after we fix some invariants. In dimension $1$, where we fix the genus, the geography question is trivial, but already in dimension $2$, it…

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…

In this paper, we firstly investigate some relations regarding the first and the second Laplace operators corresponding to the third fundamental form III of a surface in the Euclidean space E3. Besides, we introduce the finite Chen type…

In this work we are interested in the characterization of curves that belong to a given surface. To the best of our knowledge, there is no known general solution to this problem. Indeed, a solution is only available for a few examples:…

We define a Gauss map for surfaces in the universal cover of the Lie group PSL_2(R) endowed with a left-invariant Riemannian metric having a 4-dimensional isometry group. This Gauss map is not related to the Lie group structure. We prove…

Let $M$ be a compact 3-manifold with a triangulation $\tau$. We give an inequality relating the Euler characteristic of a surface $F$ normally embedded in $M$ with the number of normal quadrilaterals in $F$. This gives a relation between a…

Meridian surfaces in the Euclidean 4-space are two-dimensional surfaces which are one-parameter systems of meridians of a standard rotational hypersurface. On the base of our invariant theory of surfaces we study meridian surfaces with…

Spacelike surfaces with the same mean curvature in $\mathbb{R}^3$ and $\mathbb{L}^3$ are locally described as the graph of the solutions to the $H_R=H_L$ surface equation, which is an elliptic partial differential equation except at the…

Motivated by the large ammount of results obtained for minimal and positive constant mean curvature surfaces in several ambient spaces, the aim of this paper is to obtain half-space theorems for properly immersed surfaces in $\mathbb{R}^3$…

Canonical metrics and conformal invariants are presented for closed oriented even-dimensional manifolds with non-degenerate conformal structures and in particular for compact Riemann surfaces.

In this paper we develop an abstract theory for the Codazzi equation on surfaces, and use it as an analytic tool to derive new global results for surfaces in the space forms ${\bb R}^3$, ${\bb S}^3$ and ${\bb H}^3$. We give essentially…

A framed surface is a smooth surface in the Euclidean space with a moving frame. By using the moving frame, we can define Bertrand framed surfaces as the same idea as Bertrand framed curves. Then we find the caustics and involutes as…

In this study, we give the relationships between the conical curvatures of ruled surfaces drawn by the unit vectors of the ruling, central normal and central tangent of a regular ruled surface in the Euclidean -space. We obtain the…

Thurston parameterized quadratic invariant laminations with a non-invariant lamination, the quotient of which yields a combinatorial model for the Mandelbrot set. As a step toward generalizing this construction to cubic polynomials, we…