相关论文: On Bianchi's Backlund transformation of quadrics

In trying to generalize Bianchi's B\"acklund transformation of quadrics to B\"acklund transformations of isometric deformations of other (classes of) surfaces, we investigate basic features of the isometric deformation of surfaces via the…

We provide a generalization of Bianchi's B\"{a}cklund transformation from 2-dimensional quadrics to higher dimensional quadrics. The starting point of our investigation is the higher dimensional (infinitesimal) version of Bianchi's main…

We provide a generalization of Bianchi's triply conjugate systems containing a family of deformations of 2-dimensional quadrics together with its B\"{a}cklund transformation to higher dimensions.

We characterize Bianchi-B\"{a}cklund transformations of surfaces of positive constant Gauss curvature in terms of dressing actions of the simplest type on the space of harmonic maps.

We provide the B\"{a}cklund transforms of Peterson's isometric deformations of diagonal higher dimensional quadrics without center. These are found explicitly. can be iterated via the Bianchi Permutability Theorem and can be further…

We prove the Bianchi permutability (existence of superposition principle) of B\"acklund transformations for asymmetric quad-equations. Such equations and there B\"acklund transformations form 3D consistent systems of a priori different…

We discuss integrability of normal field equations of arbitrary parametrised Bianchi surfaces. A novel geometric definition of Bianchi surfaces is presented as well as B\"acklund transformation for the normal field equations in arbitrary…

We provide a generalization of Bianchi's Hazzidakis transformation from $2$-dimensional quadrics to generic higher dimensional quadrics.

We use the dressing method to construct transformations of constrained Willmore surfaces in arbitrary codimension. An adaptation of the Terng--Uhlenbeck theory of dressing by simple factors to this context leads us to define B\"acklund…

In trying to provide explicit deformations of quadrics the starting point of our investigation is to use Bianchi's link between real deformations of totally real regions of real paraboloids and various totally real forms of the sine-Gordon…

We study complex spatial quartic surfaces with simple singularities up to equisingular deformations; as a first step, give a complete equisingular deformation classification of the so-called non-special simple quartic surfaces.

We establish a link between Archimedes' method of integration for calculating areas, volumes and centers of mass of segments of parabolas and quadrics of revolution by factorization via the moments of a balance and an integration technique…

Backlund transformations of admissible curves in the Galilean 3-space and pseudo-Galilean 3-space and also spatial Backlund transformations of space curves in Galilean 4-space preserve the torsions under certain assumptions.

We give a complete equisingular deformation classification of simple spatial quartic surfaces which are in fact $K3$-surfaces.

We extend Painlev\'e IV model by adding quadratic terms to its Hamiltonian obtaining two classes of models (coalescence and deformation) that interpolate between Painlev\'e IV and II equations for special limits of the underlying…

We develop an essentially algebraic method to study biharmonic curves into an implicit surface. Although our method is rather general, it is especially suitable to study curves into surfaces defined by a polynomial equation: in particular,…

There is a classical geometric construction which uses a binary quadratic form to define an involution on the space of binary d-ics. We give a complete characterization of a general class of such involutions which are definable using…

It is shown that, somewhat similar to the case of classical Baecklund transformations for surfaces of constant negative curvature, infinitely many axially symmetric minimal hypersurfaces in 4-dimensional Minkowski-space can be obtained, in…

The change of conformal moduli of polygonal quadrilaterals under some geometric transformations is studied. We consider the motion of one vertex when the other vertices remain fixed, the rotation of sides, polarization, symmetrization, and…

We investigate geometric aspects of the the B\"acklund transform of principal contact element nets. A B\"acklund transform exists if and only if it the principal contact element net is of constant negative Gaussian curvature (a…