On distance-preserving transformations of lines in Euclidean three-space
The following theorem is proven: Fix \(\rho >0\) in R, and consider a bijection on the set of lines in Euclidean 3-space \(E_ 3\) such that the distance between two lines is \(\rho\) if and only if the distance between their images is \(\rho\). Then the bijection is induced by a motion of \(E_ 3\) (i.e. by an affine, distance-preserving bijection on \(E_ 3)\).
scientific article; zbMATH DE number 3884868