Related papers: A representation for pseudoholomorphic surfaces in…
In this paper we describe the $\epsilon$-isothermic surfaces in the pseudo-Euclidean 3-space and we obtain the pseudo-Calapso equation. In sequence, we classify the Dupin surfaces in pseudo-Euclidean 3-space having distinct principal…
We study special functions on euclidean spaces from the viewpoint of riemannian symmetric spaces. Here the euclidean space $E^n = G/K$ where $G$ is the semidirect product $R^n \cdot K$ of the translation group with a closed subgroup $K$ of…
The $n$-dimensional complex hyperquadric is a compact complex algebraic hypersurface defined by the quadratic equation in the $(n+1)$-dimensional complex projective space, which is isometric to the real Grassmann manifold of oriented 2-…
In this paper we prove that every open Riemann surface properly embeds in the Special Linear group $SL_2(\mathbb{C})$ as a holomorphic Legendrian curve, where $SL_2(\mathbb{C})$ is endowed with its standard contact structure. As a…
Riemann surfaces are geometric constructions in complex analysis that may represent multi-valued holomorphic functions using multiple sheets of the complex plane. We show that the energy dispersion of surface states in topological…
A proof of the uniformization theorem of Riemann surface is given with only elementary properties of holomorphic functions and not using the paracompacity of the surface. This proof leans on an holomorphic version of the topological…
The aim of this paper is to verify that the study of generic conformally flat hypersurfaces in 4-dimensional space forms is reduced to a surface theory in the standard 3-sphere. The conformal structure of generic conformally flat…
For all $k\in]0,1[$, we construct a canonical bijection between the space of ramified coverings of the sphere and the space of complete immersed surfaces in $3$-dimensional hyperbolic space of finite area and of constant extrinsic curvature…
In this article we show how holomorphic Riemannian geometry can be used to relate certain submanifolds in one pseudo-Riemannian space to submanifolds with corresponding geometric properties in other spaces. In order to do so, we shall first…
We investigate the existence of minimal hypersurfaces in $\mathbb{S}^{n+1}$ that are generated by the isoparametric foliation of a subsphere $\mathbb{S}^n$. By considering a generalized rotational ansatz formed by the union of homothetic…
We count pseudoholomorphic curves in the higher-dimensional Heegaard Floer homology of disjoint cotangent fibers of a two dimensional disk. We show that the resulting algebra is isomorphic to the Hecke algebra associated to the symmetric…
A systematic numerical framework based on Integral Equations and Generalized Sheet Transition Conditions (IE-GSTCs) is presented in 2D to synthesize closed metasurface holograms and skins for creating electromagnetic illusions of specified…
Weierstrass-type representations have been used extensively in surface theory to create surfaces with special curvature properties. In this paper we give a unified description of these representations in terms of classical transformation…
Frucht showed that, for any finite group $G$, there exists a cubic graph such that its automorphism group is isomorphic to $G$. For groups generated by two elements we simplify his construction to a graph with fewer nodes. In the general…
We consider a quadratic form defined on the surfaces with parallel mean curvature vector of an any dimensional complex space form and prove that its $(2,0)$-part is holomorphic. When the complex dimension of the ambient space is equal to…
In this paper, we characterize round spheres in the Euclidean space under some suitable conditions on the r-mean curvature.
This paper presents a unified theory for the power of a point with respect to generalized spheres (spheres, horospheres, and hyperspheres) in $n$-dimensional hyperbolic space $\mathbf{H}^n$. By extending the classical secant theorem, we…
Discrete Weierstrass-type representations yield a construction method in discrete differential geometry for certain classes of discrete surfaces. We show that the known discrete Weierstrass-type representations of certain surface classes…
A generalized Camassa-Holm equation, which describes pseudospherical surfaces, is considered. Using geometric methods, it is demonstrated that the equation is geometrically integrable. Additionally, an infinite hierarchy of conservation…
The main objective of this paper is to establish a new connection between the Hermitian rank-1 projector solutions of the Euclidean $\mathbb{C}P^{2S}$ sigma model in two dimensions and the particular hypergeometric orthogonal polynomials…