Sistemas C-ortoc\'entricos, bisectrices y euclidianidad en planos de Minkowski

TL;DR

This paper explores geometric properties of Minkowski planes, providing nine characterizations of Euclidianity based on orthogonality, bisectors, and support lines, including three generalizations and six new results.

Contribution

The paper introduces six new characterizations of Euclidianity in Minkowski planes and generalizes three existing ones for strictly convex Minkowski planes.

Findings

Nine characterizations of Euclidianity in Minkowski planes.

Three generalizations of previous characterizations for strictly convex Minkowski planes.

Six new characterizations of Euclidianity.

Abstract

Mediante el estudio de propiedades geom\'etricas de los sistemas C-ortoc\'entricos, relacionadas con las nociones de ortogonalidad (Birkhoff, is\'osceles, cordal), bisectriz (Busemann, Glogovskij) y l\'inea soporte a una circunferencia, se muestran nueve caracterizaciones de euclidianidad para planos de Minkowski arbitrarios. Tres de estas generalizan caracterizaciones dadas para planos de Minkowski estrictamente convexos en [8, 9], y las otras seis son nuevos aportes sobre el tema. -- By studying geometric properties of C-orthocentric systems related to the notions of orthogonality (Birkhoff, isosceles, chordal), angular bisector (Busemann, Glogovskij) and support line to a circumference, nine characterizations of the Euclidean plane are shown for arbitrary Minkowski planes. Three of these generalized characterizations given for strictly convex Minkowski planes in [8, 9], and the other six are new contributions on the subject.