2 citations · 5 across the 12 of their papers we have counts for
12 papers · 1 filter
On a new definition of the Bäcklund transformation in the isometric deformation of surfaces
Ion I. Dinca
We prove that a generic -dimensional integrable rolling distribution of contact elements with the symmetry of the tangency configuration (excluding developable seed and isotropi…
The Bäcklund transforms of Peterson's isometric deformations of diagonal higher dimensional quadrics without center
Ion I. Dinca
We provide the Bäcklund transforms of Peterson's isometric deformations of diagonal higher dimensional quadrics without center. These are found explicitly. can be iterated via the…
On isometric correspondence of leaves
Ion I. Dinca
We prove that for a generic -dimensional integrable rolling distribution of contact elements (excluding developable seed and isotropic developable leaves) isometric corresponden…
On the isometric deformation of surfaces via the Bäcklund transformation
Ion I. Dinca
In trying to generalize Bianchi's Bäcklund transformation of quadrics to Bäcklund transformations of isometric deformations of other (classes of) surfaces, we investigate basic fea…
On Bianchi's Backlund transformation of quadrics
Ion Dinca
We investigate basic features of Bianchi's Bäcklund transformation of quadrics to see if it can be obtained under weaker assumptions and if it can be generalized to deformations of…
Multiply conjugate systems containing deformations of quadrics
Ion I. Dinca
We provide a generalization of Bianchi's triply conjugate systems containing a family of deformations of 2-dimensional quadrics together with its Bäcklund transformation to higher…
Thread configurations for ellipsoids
Ion Dinca
We discuss Darboux-Staude type of thread configurations for the ellipsoid similar to Chasles-Graves type of thread configurations for the ellipse. These threads are formed by recti…
Bianchi's Bäcklund transformation for higher dimensional quadrics
Ion I. Dinca
We provide a generalization of Bianchi's Bäcklund transformation from 2-dimensional quadrics to higher dimensional quadrics. The starting point of our investigation is the higher d…
The Bäcklund transforms of Peterson's deformations of quadrics
Ion I. Dinca
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 pa…
Peterson's Deformations of Higher Dimensional Quadrics
Ion I. Dinca
We provide the first explicit examples of deformations of higher dimensional quadrics: a straightforward generalization of Peterson's explicit 1-dimensional family of deformations…
Archimedes' balance and Bianchi's Backlund transformation for quadrics
Ion Dinca
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 factorizatio…
The Method of Archimedes in the geometry of quadrics
Ion I. Dinca
Confocal quadrics capture (encode) and geometrize spectral properties of symmetric operators. Certain metric-projective properties of confocal quadrics (most of them established in…