Weighted projective spaces and a generalization of Eves' theorem
Adam Coffman
article abstract
For a certain class of configurations of points in space, Eves'
Theorem gives a ratio of products of distances that is invariant under
projective transformations, generalizing the cross-ratio for four
points on a line. We give a generalization of Eves' theorem, which
applies to a larger class of configurations and gives an invariant
with values in a weighted projective space. We also show how the
complex version of the invariant can be determined from classically
known ratios of products of determinants, while the real version of
the invariant can distinguish between configurations that the
classical invariants cannot.
addendum:
An online-only, 2-page addendum appears on the journal web site.