Characterizations of finite classical polar spaces by intersection numbers with hyperplanes and spaces of codimension 2 (Q532121)

The following is the main result of the paper. Theorem. Let \(P\) be a non-singular quadric or Hermitian variety of a finite projective space PG\((n,q)\), where \(n \geq 4\) and \(q > 2\). If \(X\) is a set of points of PG\((n,q)\) having the same intersection numbers with hyperplanes and subspaces of co-dimension 2 of \({PG}(n,q)\), then \(X\) is projectively equivalent with \(P\).