Curves in the Minkowski plane and their geometry

Plática dada por Alex Paulo Francisco (ICMC-USP, Brazil) en el Singularities in generic geometry and its applications: Valencia V, para celebrar el 60 aniversario de Federico Sánchez Bringas en agosto del 2017 en el Auditorio Carlos Graef del Amoxcalli en la Facultad de Ciencias de la UNAM

Abstract:
The equivalence relation by the A is very important for studying singularities of map-germs, in particular, when we study the deformations of singularities of plane curves. However, if we are interested in the geometry of curves, then this relation is not very appropriate, since diffeomorphisms do not preserve their geometry. Hence arose the need to define deformations which preserves the geometry of curves. In [SALARINOGHABI, M.; TARI,
F. Flat and round singularity theory of plane curves. Preprint, 2015.], such deformations were called FRS-deformations, from which it was possible to obtain a way to study the bifurcations of a curve in the Euclidian plane taking into account its geometry (inflections, vertices and singularities).
Our goal is to consider the above questions in the case of curves in the Minkowski plane. We note that the geometric consequences of the contact of a curve with pseudo-circles in the Minkowski plane are different of the contact of a curve with a circle in the Euclidian plane, as, for example, the behavior of the caustic.
In this work we define the FRLS-equivalence of curves in the Minkowski plane and we analyzed the deformations of curves and the bifurcation of its caustics in the Minkowski plane around specific points, such as vertices, inflections and lightlike points.

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