相关论文: Bianchi surfaces. Integrability in arbitrary param…

We study endomorphism rings of principally polarized abelian surfaces over finite fields from a computational viewpoint with a focus on exhaustiveness. In particular, we address the cases of non-ordinary and non-simple varieties. For each…

We present a general analysis of the field theoretical properties which guarantee the recovery, at the renormalized level, of symmetries broken by regularization. We also discuss the anomalous case.

A procedure for interpolating between specified points of a curve or surface is described. The method guarantees slope continuity at all junctions. A surface panel divided into p x q contiguous patches is completely specified by the…

The algebraic translational surface is a typical modeling surface in computer aided design and architecture industry. In this paper, we give a necessary and sufficient condition for that algebraic surface having a standard parametric…

Along this work we study an indefinite abstract smoothing problem. After establishing necessary and sufficient conditions for the existence of solutions to this problem, the set of admissible parameters is discussed in detail. Then, its…

: Algebraic properties of orbifold models on arbitrary Riemann surfaces are investigated. The action of mapping class group transformations and of standard geometric operations is given explicitly. An infinite dimensional extension of the…

We present an algorithm that covers any given rational ruled surface with two rational parametrizations. In addition, we present an algorithm that transforms any rational surface parametrization into a new rational surface parametrization…

For abelian surfaces of Picard rank 1, we perform explicit computations of the cohomological rank functions of the ideal sheaf of one point, and in particular of the basepoint-freeness threshold. Our main tool is the relation between…

We show that any analytically integrable Hamiltonian system near an equilibrium point admits a convergent Birkhoff normalization. The proof is based on a new, geometric approach to the problem.

We discuss methods to construct a polynomial parametrization of some interesting knotted surfaces (knotted spheres, knotted tori and knotted planes) and provide examples.

A Darboux transformation for polarized space curves is introduced and its properties are studied, in particular, Bianchi permutability. Semi-discrete isothermic surfaces are described as sequences of Darboux transforms of polarized curves…

Singular complex analytic vector fields on the Riemann surfaces enjoy several geometric properties (singular means that poles and essential singularities are admissible). We describe relations between singular complex analytic vector fields…

In this paper, we define a new conformal invariant on complete non-compact hyperbolic surfaces that can be conformally compactified to bounded domains in $\mathbb{C}$. We study and compute this invariant up to one-connected surfaces. Our…

This note derives parametrizations for surfaces of revolution that satisfy an affine-linear relation between their respective curvature radii. Alongside, parametrizations for the uniform normal offsets of those surfaces are obtained. Those…

We give an elegant formulation of the structure equations (of Cartan) and the Bianchi identities in terms of exterior calculus without reference to a particular basis and without the exterior covariant derivative. This approach allows both…

Treating an integrable quad-equation along with its two generalised symmetries as a compatible system allows one to construct an auto-B\"acklund transformation for solutions of the related NLS-type system. A fixed periodic reduction of the…

We present the constraint for the discrete Moutard equation which gives the integrable discretization of the Bianchi-Ernst system. We also derive the discrete analogue of the Bianchi transformation between solutions of such a system (the…

The paper presents the bosonic and fermionic supersymmetric extensions of the structural equations describing conformally parametrized surfaces immersed in a Grasmann superspace, based on the authors' earlier results. A detailed analysis of…

We study the Hamiltonian formulation for a parametrized scalar field in a regular bounded spatial region subject to Dirichlet, Neumann and Robin boundary conditions. We generalize the work carried out by a number of authors on parametrized…

The geometry of an admissible B\"acklund transformation for an exterior differential system is described by an admissible Cartan connection for a geometric structure on a tower with infinite--dimensional skeleton which is the universal…