Related papers: A representation formula for non-conformal harmoni…
We find a spinorial representation of a Riemannian or Lorentzian surface in a Lorentzian homogeneous space of dimension $3.$ We in particular obtain a representation theorem for surfaces in the $\mathbb{L}(\kappa,\tau)$ spaces. We then…
We study harmonic surfaces in $\mathbb{R}^3$ through the framework of harmonic Enneper immersions and prove a superposition principle for such surfaces. We prove that minimal and maximal surfaces admit a decomposition into harmonic…
The current paper discusses some new results about conformal polynomic surface parameterizations. A new theorem is proved: Given a conformal polynomic surface parameterization of any degree it must be harmonic on each component. As a first…
For closed and oriented hyperbolic surfaces, a formula of Witten establishes an equality between two volume forms on the space of representations of the surface in a semisimple Lie group. One of the forms is a Reidemeister torsion, the…
As an example of a noncommutative space we discuss the quantum 3-dimensional Euclidean space $R^3_q$ together with its symmetry structure in great detail. The algebraic structure and the representation theory are clarified and discrete…
We prove a Simons type equation for non-minimal surfaces with parallel mean curvature vector (pmc surfaces) in $M^n(c)\times\mathbb{R}$, where $M^n(c)$ is an $n$-dimensional space form. Then, we use this equation in order to characterize…
We study rotational surfaces in Euclidean 3-space whose Gauss curvature is given as a prescribed function of its Gauss map. By means of a phase plane analysis and under mild assumptions on the prescribed function, we generalize the…
In this article we consider PMC surfaces in complex space forms, and we study the interaction between the notions of PMC, totally real and biconservative. We first consider PMC surfaces in non-flat complex space forms and we prove that they…
We consider N-point deformation of algebraic K3 surfaces. First, we construct two-point deformation of algebraic K3 surfaces by considering algebraic deformation of a pair of commutative algebraic K3 surfaces. In this case, the moduli space…
We find a system of two polynomial equations in two unknowns, whose solution allows to give an explicit expression of the conformal representation of a simply connected three sheeted compact Riemann surface onto the extended complex plane.…
Applying Morse theory, we give a standard form for a class of surfaces which includes all the properly embedded incompressible surfaces in 3-dimensional handlebodies. We also give a necessary and sufficient condition to determine the…
The representations of the algebra of coordinates and momenta of noncommutative phase space are given. We study, as an example, the harmonic oscillator in noncommutative space of any dimension. Finally the map of Sch$\ddot{o}$dinger…
We characterize the Artin invariant of a smooth K3 hypersurface in terms of quasi-$F$-splitting. As an application, we obtain an explicit formula for this invariant.
Representations of four-dimensional superconformal groups on harmonic superfields are discussed. It is argued that any representation can be given as a superfield on many superflag manifolds. Representations on analytic superspaces do not…
Hypersurfaces embedded in conformal manifolds appear frequently as boundary data in boundary-value problems in cosmology and string theory. Viewed as the non-null conformal infinity of a spacetime, we consider hypersurfaces embedded in a…
In this note we present the classification of non-symplectic automorphisms of prime order on K3 surfaces, i.e.we describe the topological structure of their fixed locus and determine the invariant lattice in cohomology. We provide new…
In this paper we introduce the notion of timelike surface with harmonic inverse mean curvature in 3-dimensional Lorentzian space forms, and study their fundamental properties.
We use functions of a bicomplex variable to unify the existing constructions of harmonic morphisms from a 3-dimensional Euclidean or pseudo-Euclidean space to a Riemannian or Lorentzian surface. This is done by using the notion of…
In this paper, we study oriented surfaces S in $\mathbb{R}^3$, called Surfaces with quadratic support function of harmonic type (in short HQSF-surfaces), these surfaces generalize the QSF-surfaces. We obtain a Weierstrass type…
We present infinitely many nonlocal conservation laws, a pair of compatible local Hamiltonian structures and a recursion operator for the equations describing surfaces in three-dimensional space that admit nontrivial deformations which…