Isometry Classes of Planes in $(\mathbb{R}^3,d_{\infty})$
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 $\mathbb{R}_{\infty}^3$.
math.MG↗
arXiv subjects
Publications and source records attributed to Mehmet Kılıç.
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 $\mathbb{R}_{\infty}^3$.
We give a simple algorithm for the construction of the tight span of a finite subset of the Manhattan plane.