Related papers: Weierstrass-type representations
In this paper we give Weierstrass-type representation formulas for the null curves and for the minimal Lorentz surfaces in the Minkowski 3-space $\mathbb R^3_1$ using real-valued functions. Applying the Weierstrass-type representations for…
We use Weierstrass Point Theory and Frobenius orders to prove the uniqueness (up to isomorphism) of some optimal curves.
A new approach is proposed for study structure and properties of the total squared mean curvature $W$ of surfaces in ${\bf R}^3$. It is based on the generalized Weierstrass formulae for inducing surfaces. The quantity $W$ (Willmore…
Given a unit vector field on a closed Euclidean hypersurface, we define a map from the hypersurface to a sphere in the Euclidean space. This application allows us to exhibit a list of topological invariants which combines the second…
Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an…
In this paper we demonstrate that the notion of inflection points and extactic points on plane algebraic curves can be suitably transferred to curves in $\mathbb{P}^1\times \mathbb{P}^1$. More precisely, we describe osculating curves and…
In hyperbolic 3-space $\mathbb{H}^3$ surfaces of constant mean curvature $H$ come in three types, corresponding to the cases $0 \leq H < 1$, $H = 1$, $H > 1$. Via the Lawson correspondence the latter two cases correspond to constant mean…
Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.
The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…
We develop the theory of Wigner representations for general probabilistic theories (GPTs), a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way…
We introduce curvature-adapted foliations of complex hyperbolic space and study some of their properties. Generalized pseudo-Einstein hypersurfaces of complex hyperbolic space are classified. Analogous results for curvature-adapted…
Soliton surfaces associated with CP^{N-1} sigma models are constructed using the Generalized Weierstrass and the Fokas-Gel'fand formulas for immersion of 2D surfaces in Lie algebras. The considered surfaces are defined using continuous…
Minimal surfaces with isothermal parameters admitting B\'{e}zier representation were studied by Cosin and Monterde. They showed that, up to an affine transformation, the Enneper surface is the only bi-cubic isothermal minimal surface. Here…
In this paper Witten type deformation of osp(1/2) algbera is introduced and its realization and matrix representation are obtained. The matrix representation is shown to be possible only when the dimension is odd.
We develop a homotopical variant of the classic notion of an algebraic theory as a tool for producing deformations of homotopy theories. From this, we extract a framework for constructing and reasoning with obstruction theories and spectral…
We study the twist-field representations of W-algebras and generalize construction of the corresponding vertex operators to D- and B-series. It is shown, how the computation of characters of these representations leads to nontrivial…
We introduce a new class of surfaces in Euclidean $3$-space, called surfaces of osculating circles, using the concept of osculating circle of a regular curve. These surfaces contain a uniparametric family of planar lines of curvature. In…
We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the…
Over the past two decades the theory of the Weil-Petersson metric has been extended to general Teichm\"uller spaces of infinite type, including for example the universal Teichm\"uller space. In this paper we give a survey of the main…
In this paper we characterize compact and complete hypersurfaces with some constant higher order mean curvature into warped product spaces. Our approach is based on the use of a new trace operator version of the Omori-Yau maximum principle…