A CHARACTERISATION OF EUCLIDEAN NORMED PLANES VIA BISECTORS. Issue 1 (20th August 2018) - CABELLO SÁNCHEZ, JAVIER; GORDILLO-MERINO, ADRIÁN
Abstract : Our main result states that whenever we have a non-Euclidean norm · on a two-dimensional vector space X, there exists some x≠ 0 such that for every [STIX]x1D706≠ 1, [STIX]x1D706>0, there exist y, zX satisfying y=[STIX]x1D706x, z≠ 0 and z belongs to the bisectors B(-x, x) and B(-y, y) . We also give several results about the geometry of the unit sphere of strictly convex planes.