Related papers: Affine Factorable Surfaces in Pseudo-Galilean Spac…
Detailed analysis of scanning probe microscopy (SPM) data acquired for faceted and non-flat surfaces is usually complicated due to the presence of a large number of surface areas tilted by large/variable angles relative to the scanning…
Let $\mathcal{X}$ be a projective algebraic curve and denote by $\mathcal{X}^{'}$ its strict dual curve. The map $\gamma:\mathcal{X} \longrightarrow \mathcal{X}^{'}$ is called (strict) Gauss map of $\mathcal{X}$. In this manuscript, we…
This paper is concerned with the mean curvature flow, which describes the dynamics of a hypersurface whose normal velocity is determined by local mean curvature. We present a Cartesian grid-based method for solving mean curvature flows in…
A homothetical surface arises as a graph of a function $z = \varphi_1(v_1) \varphi_2(v_2)$. In this paper, we study the homothetical surfaces in three dimensional psuedo-Galilean space$\left(\mathbb{G}_3^1\right)$ satisfying the conditions…
We examine a simple hard disc fluid with no long range interactions on the two dimensional space of constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is…
We consider systems of partial differential equations of the form \begin{equation}\nonumber \left\{ \begin{array}{l} u_{xt}=F\left(u,u_x,v,v_x\right),\\ v_{xt}=G\left(u,u_x,v,v_x\right), \end{array} \right. \end{equation} describing…
A class of surfaces-graphs in a Riemannian 3-space with a prescribed projection of one field of principal directions onto a surface $\Pi$ is considered. A problem of determination of such surfaces when both principal curvatures are given…
We consider a finite difference approximation of mean curvature flow for axisymmetric surfaces of genus zero. A careful treatment of the degeneracy at the axis of rotation for the one dimensional partial differential equation for a…
We present a computational scheme that derives a global polynomial level set parametrisation for smooth closed surfaces from a regular surface-point set and prove its uniqueness. This enables us to approximate a broad class of smooth…
We give a criterion for certain generic nondegenerate surfaces in a fake weighted projective $3$-space to have Picard number $>1$. These algebraic surfaces are of general type. We do this by considering degenerations (along an edge),…
We consider the Gauss curvature type flow for uniformly convex hypersurfaces in the hyperbolic space $\mathbb{H}^{n+1}\ (n\geqslant 2)$. We prove that if the initial closed hypersurface is smooth and uniformly convex, then the smooth…
We discuss the local differential geometry of convex affine spheres in $\re^3$ and of minimal Lagrangian surfaces in Hermitian symmetric spaces. In each case, there is a natural metric and cubic differential holomorphic with respect to the…
We define and discuss the notion of pseudospherical surfaces in asymptotic coordinates on time scales. Two special cases, namely dicrete pseudospherical surfaces and smooth pseudosperical surfaces are consistent with this description. In…
In this paper, first and second type admissible Mannheim partner curves are defined in pseudo-Galilean space $G_3^1$. Moreover, it is proved that the distance between the reciprocal points of both of first and second type admissible…
We survey different classification results for surfaces with parallel mean curvature immersed into some Riemannian homogeneous four-manifolds, including real and complex space forms, and product spaces. We provide a common framework for…
We make a systematic study of the focal surface of a congruence of lines in the projective space. Using differential techniques together with techniques from intersection theory, we reobtain in particular all the invariants of the focal…
Surfaces of finite geometric type are complete, immersed into the tree-dimensional Euclidean space with finite total curvature and Gauss map extending to an oriented compact surface as a smooth branched covering map over the unit sphere of…
In this series of papers we aim to provide a mathematically comprehensive framework to the Hamiltonian pictures of quantum field theory in curved spacetimes. Our final goal is to study the kinematics and the dynamics of the theory from the…
In a previous work, the authors gave a definition of `front bundles'. Using this, we give a realization theorem for wave fronts in space forms, like as in the fundamental theorem of surface theory. As an application, we investigate the…
A class of two-dimensional superintegrable systems on a constant curvature surface is considered as the natural generalization of some well known one-dimensional factorized systems. By using standard methods to find the shape-invariant…