Recognizable classification of Lorentzian distance-squared mappings (Q2448259)

For finitely many points \(p_0,\dots ,p_k \in \mathbb{R}^{1,n} (1\leq k)\), the authors define the Lorentzian distance-squared mappings by \[ L_{(p_0,\dots ,p_k)} : \mathbb{R}^{1,n} \rightarrow \mathbb{R}^{k+1}, L_{(p_0,\dots ,p_k)}(x)=(l_{p_0}^2(x),\dots ,l_{p_k}^2(x)), \] where \(l_{p}^2\) is the standard Lorentzian distance squared-function. The main result of the paper is the classification of these mappings completely by using recognition subspaces (Theorem 1).