Talk:Projective orthogonal group

PO is the group of isometries of *elliptic space*, not projective space
> More intrinsically, the (real positive definite) projective orthogonal group PO can be defined as the isometries of real projective space, while PSO can be defined as the orientation-preserving isometries of real projective space (when the space is orientable; otherwise PSO = PO).

Projective space doesn't normally have a metric. When it's endowed with the proper metric, it becomes known as elliptic space in the sense of elliptic geometry. Shouldn't this article be changed so that every mention of projective space is replaced with elliptic space? --Svennik (talk) 16:35, 18 July 2021 (UTC)