On F-regular m-tuples in complex projective spaces (Q1126445)

The author investigates \(F\)-regular \(m\)-tuples of points in the complex projective space \(\mathbb{C} P^n\), \(3\leq m-1\leq n\). A finite set of \(m\) points in \(\mathbb{C} P^n\) is called \(F\)-regular if all ordered triples of points which are contained in it are pairwise isometric. It is shown that for a given triangle \(T\) there exist at most two isometry classes of \(F\)-regular 5- tuples containing \(T\). The author also studies \(k\)-regular \(m\)- tuples. These are \(F\)-regular \(m\)-tuples in which all \(k\)-tuples are pairwise isometric. One of the results is that 4-regularity implies \(k\)-regularity for \(k\geq 5\).