Hyperplane sections of polar spaces (Q1184580)

Let \(\gamma=(P,{\mathcal L},I)\) be a finite, classical non-degenerate polar space of rank at least 2 defined by means of a sesquilinear or quadratic form on a finite vector space \(V\), and let \(X\subset P\) such that \(| 1\cap X|\neq 0,2\) for any \(1\bar\in{\mathcal L}\). There is a natural embedding of \(\gamma\) into \(PG(V)\). The author shows that if \(\gamma\) is not of rank 2 or \(X\) is not an ovoid then \(X\) is the intersection of \(P\) with a hyperplane of \(PG(V)\).