6 citations · 15 across the 7 of their papers we have counts for
7 papers
On Surfaces in R^n via Gauss Map, Caustics, Duality and Pseudo Euclidean Geometry of Quadratic Forms
Ricardo Uribe-Vargas
We get new results (and rederive some know ones) on smooth surfaces in by unifying several view points into a coherent general view. Namely, we show and use new rela…
Contact with circles and Euclidean invariants of smooth surfaces in R^3
Peter Giblin, Graham Reeve, Ricardo Uribe-Vargas
We investigate the vertex curve, that is the set of points in the hyperbolic region of a smooth surface in real 3-space at which there is a circle in the tangent plane having at le…
Evolving Surfaces and Evolving Implicit Differential Equations Via Contact Geometry and Singularities
Ricardo Uribe-Vargas
We present the list of unavoidable local phenomena (transitions) occurring on the configuration of the parabolic and flecnodal curves of evolving smooth surfaces in R^3 (or RP^3).…
Characteristic Points, Fundamental Cubic Form and Euler Characteristic of Projective Surfaces
Maxim Kazarian, Ricardo Uribe-Vargas
We define local indices for projective umbilics and godrons (also called cusps of Gauss) on generic smooth surfaces in projective 3-space. By means of these indices, we provide for…
On Projective Umbilics: a Geometric Invariant and an Index
Ricardo Uribe-Vargas
We define a geometric invariant and an index (+1 or -1) for projective umbilics of smooth surfaces. We prove that the sum of the indices of the projective umbilics inside a connect…
On Vertices and Focal Curvatures of Space Curves
Ricardo Uribe-Vargas
The {\em focal curve} of an immersed smooth curve , in Euclidean space , consists of the centres of its osculating hyperspheres. The focal curve may be p…
A New Projective Invariant Associated to the Special Parabolic Points of Surfaces and to Swallowtails
Ricardo Uribe-Vargas
We show some generic (robust) properties of smooth surfaces immersed in the real 3-space (Euclidean, affine or projective), in the neighbourhood of a {\em godron} (term due to R.Th…