Isometry Classes of Planes in $({\mathbb{R}}^3,d_{\infty })$

Abstract

We determine geodesics in ${\mathbb{R}}_{\infty }^n$ (i.e. $({\mathbb{R}}^n,d_{\infty })$) and by using this, classify planes up to isometry in ${\mathbb{R}}_{\infty }^3$.