相关论文: Natural PDE's of Linear Fractional Weingarten surf…

In this paper, we study a natural discretization of the smooth Gaussian curvature on surfaces, which is defined as the quotient of the angle defect and the area of a geodesic disk at a vertex of a polyhedral surface. It is proved that each…

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…

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…

We study quotients of quadratic forms and associated polar lines in the projective plane. Our results, applied pointwise to quadratic differential forms, shed some light on classical binary differential equations (BDEs) associated to…

This is a preliminary note on a family of minimal surfaces in the 3-sphere defined by a compatible fourth order equation. The minimal surfaces are geometrically characterized either by having a surface of revolution like induced metric, or…

Progressive addition lenses contain a surface of spatially-varying curvature, which provides variable optical power for different viewing areas over the lens. We derive complete compatibility equations that provide the exact magnitude of…

To each del Pezzo surface (resp. ruled surface, ruled surface with a section), we describe a natural Lie algebra bundle of type E_n (resp. D_n, A_n) over it. Using lines and rulings on any such surface, we describe various representation…

In this paper we classify Weingarten surfaces integrable in the sense of soliton theory. The criterion is that the associated Gauss equation possesses an sl(2)-valued zero curvature representation with a nonremovable parameter. Under…

In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map of Weingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type…

Minimal surfaces with planar curvature lines in the Euclidean space have been studied since the late 19th century. On the other hand, the classification of maximal surfaces with planar curvature lines in the Lorentz-Minkowski space has only…

We interpret a normal surface in a (singular) three-manifold in terms of the homology of a chain complex. This allows us to study the relation between normal surfaces and their quadrilateral co-ordinates. Specifically, we give a proof of an…

We consider a special family of 2-dimensional timelike surfaces in the Minkowski 4-space $\mathbb{R}^4_1$ which lie on rotational hypersurfaces with timelike axis and call them meridian surfaces of elliptic type. We study the following…

A space-like surface in Minkowski space-time is minimal if its mean curvature vector field is zero. Any minimal space-like surface of general type admits special isothermal parameters - canonical parameters. For any minimal surface of…

We study compact stable embedded minimal surfaces whose boundary is given by two collections of closed smooth Jordan curves in close planes of Euclidean 3-space. Our main result is a classification of these minimal surfaces, under certain…

In this paper, we derive the first variation formulas for surfaces in 3-dimensional Euclidean space by using the ``strain-displacement relations'' known in thin shell theory. For applications to architectural surface design, we focus on the…

The study of the relation between the Weierstrass inducing formulae for constant mean curvature surfaces and the completely integrable euclidean nonlinear sigma-model suggests a connection among integrable sigma -models in a background and…

Discrete normal surfaces are normal surfaces whose intersection with each tetrahedron of a triangulation has at most one component. They are also natural Poincar\'e duals to 1-cocycles with $\ZZ/2\ZZ$-coefficients. For a fixed cohomology…

A submanifold of a pseudo-Riemannian manifold is said to have parallel mean curvature vector if the mean curvature vector field H is parallel as a section of the normal bundle. Submanifolds with parallel mean curvature vector are important…

We introduce canonical principal parameters on any strongly regular minimal surface in the three dimensional sphere and prove that any such a surface is determined up to a motion by its normal curvature function satisfying the Sinh-Poisson…

A canonical normal null direction on a spacelike surface in the four dimensional Minkowski space $\mathbb{R}^{3,1}$ is a parallel vector field $Z$ on $\mathbb{R}^{3,1}$ such that the normal component of $Z$ on the surface is a lightlike…