8 papers · 1 filter
Singularities of Discrete Indefinite Affine Minimal Surfaces
Marcos Craizer
A smooth affine minimal surface with indefinite metric can be obtained from a pair of smooth non-intersecting spatial curves by Lelieuvre's formulas. These surfaces may present sin…
Moutard hyperquadrics and generalized Darboux directions
Fernanda Py Silva Cordeiro, Marcos Craizer
The higher order contact of a quadric with a surface in -space at a non-degenerate point is obtained by the Moutard quadric in the Darboux direction. In this paper, we discuss t…
Affine focal sets of codimension submanifolds contained in hyper surfaces
Marcos Craizer, Marcelo J. Saia, Luis F. Sánchez
In this paper we study the affine focal set, which is the bifurcation set of the affine distance to submanifolds contained in hypersurfaces of the -space. We…
Equiaffine Characterization Of Lagrangian Surfaces in
Marcos Craizer
For non-degenerate surfaces in , a distinguished transversal bundle called affine normal plane bundle was proposed in [Nomizu-Vrancken]. Lagrangian surfaces have remarkable pr…
Curvature Motion in a Minkowski Plane
Vitor Balestro, Marcos Craizer, Ralph C. Teixeira
In this paper we study the curvature flow of a curve in a plane endowed with a minkowskian norm whose unit ball is smooth. We show that many of the properties known in the euclidea…
Involutes of Polygons of Constant Width in Minkowski Planes
Marcos Craizer, Horst Martini
Consider a convex polygon P in the plane, and denote by U a homothetical copy of the vector sum of P and (-P). Then the polygon U, as unit ball, induces a norm such that, with resp…