6 citations · 6 across the 6 of their papers we have counts for
6 papers
New Properties and Invariants of Harmonic Polygons
Ronaldo Garcia, Dan Reznik, Pedro Roitman
Via simulation, we discover and prove curious new Euclidean properties and invariants of the Poncelet family of harmonic polygons.
New Invariants of Poncelet-Jacobi Bicentric Polygons
Pedro Roitman, Ronaldo Garcia, Dan Reznik
The 1d family of Poncelet polygons interscribed between two circles is known as the Bicentric family. Using elliptic functions and Liouville's theorem, we show (i) that this family…
Hypersurfaces of Product Spaces with a Canonical Direction
Ronaldo F. de Lima, Pedro Roitman
Consider a complete Riemannian manifold and let be an orientable hypersurface of the product manifold endowed with its standard product metric $\lan…
A connection between flat fronts in hyperbolic space and minimal surfaces in euclidean space
Antonio Martínez, Pedro Roitman, Keti Tenenblat
A geometric construction is provided that associates to a given flat front in a pair of minimal surfaces in which are related by a Ribaucour transform…
A class of surfaces related to a problem posed by Élie Cartan
Antonio Martínez, Pedro Roitman
We introduce a class of surfaces in euclidean space motivated by a problem posed by Élie Cartan. This class furnishes what seems to be the first examples of pairs of non-congruent…
CMC-1 Surfaces in Hyperbolic 3-space using the Bianchi-Calo method
Levi Lopes de Lima, Pedro Roitman
In this note we present a method for constructing CMC-1 surfaces in hyperbolic 3-space $\bfH^3(-1)$ in terms of holomorphic data first introduced in Bianchi's Lezioni di Geometria…