It is known that in projective transformations the distance does not have to remain invariant as it occurs in Euclidean Geometry with isometries.
However, I have found an article called Geometries of the projective matrix space (see https://core.ac.uk/download/pdf/82526440.pdf), in which he points out :"The projectivity S keeps the Euclidean distance invariant if and only if the corresponding matrices Y are of the form where s # 0 is an arbitrary complex number". This contrasts with what was said in How to define a "distance" from point to line in 3D projective space which is projectively invariant? My question is: is it possible to find a projectivity in some plane or projective space that keeps the Euclidean distance invariant? Where can I find an article about it, in addition to the one already mentioned? Thank you so much.
