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- Title
A CHARACTERISATION OF EUCLIDEAN NORMED PLANES VIA BISECTORS.
- Authors
CABELLO SÁNCHEZ, JAVIER; GORDILLO-MERINO, ADRIÁN
- Abstract
Our main result states that whenever we have a non-Euclidean norm $\Vert \cdot \Vert$ on a two-dimensional vector space $X$ , there exists some $x\neq 0$ such that for every $\unicode[STIX]{x1D706}\neq 1$ , $\unicode[STIX]{x1D706}>0$ , there exist $y,z\in X$ satisfying $\Vert y\Vert =\unicode[STIX]{x1D706}\Vert x\Vert$ , $z\neq 0$ 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.
- Subjects
NON-Euclidean geometry; VECTOR spaces; FUNCTION algebras; POLYNOMIALS; BISECTORS (Geometry)
- Publication
Bulletin of the Australian Mathematical Society, 2019, Vol 99, Issue 1, p121
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972718000758