相关论文: On the isometric deformation of surfaces via the B…

We investigate basic features of Bianchi's B\"acklund transformation of quadrics to see if it can be obtained under weaker assumptions and if it can be generalized to deformations of other surfaces.

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 that for a generic $3$-dimensional integrable rolling distribution of contact elements (excluding developable seed and isotropic developable leaves) isometric correspondence of leaves of a general nature (independent of the shape…

We prove that a generic $4$-dimensional integrable rolling distribution of contact elements with the symmetry of the tangency configuration (excluding developable seed and isotropic developable leaves) splits into an $1$-dimensional family…

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

This work is dedicated to the study of the Moebius invariant class of constrained Willmore surfaces and its symmetries. We define a spectral deformation by the action of a loop of flat metric connections; Baecklund transformations, by…

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…

Isothermic surfaces are surfaces which allow a conformal curvature line parametrisation. They form an integrable system, and Darboux transforms of isothermic surfaces obey Bianchi permutability: for two distinct spectral parameters the…

We study infinitesimal conformal deformations of a triangulated surface in Euclidean space and investigate the change in its extrinsic geometry. A deformation of vertices is conformal if it preserves length cross-ratios. On one hand,…

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…

The notion of a generalized harmonic inverse mean curvature surface in the Euclidean four-space is introduced. A backward B\"{a}cklund transform of a generalized harmonic inverse mean curvature surface is defined. A Darboux transform of a…

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…

We construct models of involution surface bundles over algebraic surfaces, degenerating over normal crossing divisors, and with controlled singularities of the total space.

In this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we prove a criterion that determines when a finite…

The new integrable mapping with a simple geometric interpretation is presented. This mapping arise from the nonlinear superposition principle for the B\"acklund transformations of some vector evolution equation.

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…

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.