Related papers: Poncelet Spatio-Temporal Surfaces and Tangles
The problem of construction of the surfaces with given sets of the points with horizontal tangential planes is considered. Such considerations are of interest in the problem of computer simulations of the waved ocean surfaces.
We give an up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds. We also mention some of their applications to time-dependent mechanics.
We give a brief introduction to some of the recent works on finding geometric structures on triangulated surfaces using variational principles.
In this note we briefly review some recent results of the authors on the topological and geometrical properties of 3-cosymplectic manifolds.
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…
In this study we give definitions and characterizations of transversal surfaces of timelike ruled surfaces. We study some special cases such as the striction curve is a geodesic, an asymptotic line or a line of curvature. Moreover, we…
In this paper we classify certain special ruled surfaces in $\R^3$ under the general theorem of characterization of constant angle surfaces. We study the tangent developable and conical surfaces from the point of view the constant angle…
We classify the singular loci of real surfaces in three-space that contain two circles through each point. We characterize how a circle in such a surface meets this loci as it moves in its pencil and as such provide insight into the…
We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…
K3 surfaces have been studied from many points of view, but the positivity of the cotangent bundle is not well understood. In this paper we explore the surprisingly rich geometry of the projectivised cotangent bundle of a very general…
We survey some results on real rational surfaces focused on their topology and their birational geometry.
We characterize singularities of focal surfaces of wave fronts in terms of differential geometric properties of the initial wave fronts. Moreover, we study relationships between geometric properties of focal surfaces and geometric…
We discuss various phenomena of tangency in projective and convex geometry.
This survey gives a brief overview of theoretically and practically relevant algorithms to compute geodesic paths and distances on three-dimensional surfaces. The survey focuses on polyhedral three-dimensional surfaces.
Given a trivalent graph in the 3-dimensional Euclidean space, we call it a discrete surface because it has a tangent space at each vertex determined by its neighbor vertices. To abstract a continuum object hidden in the discrete surface, we…
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…
This work investigates slant timelike-ruled surfaces and their evolute offsets in Minkowski 3-space $\mathbb{E}_{1}^{3}$. Using the symmetry of evolute curves, we derive a parametric formulation for skew timelike-ruled surfaces and…
In this paper we study topological surfaces as gridded surfaces in the 2-dimensional scaffolding of cubic honeycombs in Euclidean and hyperbolic spaces.
We study the geometry and topology of immersed surfaces in Euclidean 3-space whose Gauss map satisfies a certain two-piece-property, and solve the ``shadow problem" formulated by H. Wente.
We describe a newly-developed, free, browser-based application, for the interactive exploration of the dynamic geometry of Poncelet families of triangles. The main focus is on responsive display of the beauteous loci of centers of such…