Elliptic inversion in \(l_\infty\)-plane. (English) Zbl 07923746
Summary: In this study, we introduce elliptic inversion and investigate general properties and basic concepts of this inversion in \(l_\infty\)-plane or \(\mathbb{R}^2_M\), the plane equipped with the \(l_\infty\)-metric. In addition, we give some properties such as cross ratio and harmonic conjugates of the elliptic inversion in \(l_\infty\)-plane or \(\mathbb{R}^2_M\).
MSC:
| 51B20 | Minkowski geometries in nonlinear incidence geometry |
| 51N25 | Analytic geometry with other transformation groups |
| 51F99 | Metric geometry |
| 51K05 | General theory of distance geometry |
| 51K99 | Distance geometry |
| 52A15 | Convex sets in \(3\) dimensions (including convex surfaces) |
| 52B10 | Three-dimensional polytopes |
