Zur Kennzeichnung der Kollineationen zwischen Quadriken. (On the characterization of collineations between quadrics) (Q1102534)

Given two pappian projective spaces P and P' of finite dimension \(n\geq 3\) whose coordinate fields are both of characteristic \(\neq 2\), the author examines bijections \(\Phi\) between quadrics of same rank and index \(Q^{n-1}\), \(Q^{'n-1}\) in P, resp. P'. She applies a theorem of \textit{R. Wagner} [Math. Z. 83, 336-344 (1964; Zbl 0117.378)] to prove: Suppose that \(Q^{n-1}\), and \(Q^{'n-1}\) have an index \(\neq 0\). Then there exists a unique collineation \(P\to P'\) extending \(\Phi\) iff \(\Phi\) maps the (n-2)-dimensional quadrics of maximal rank in \(Q^{n-1}\) onto those of maximal rank in \(Q^{'n-1}.\) She mentions an application of this to the semilinearization of sphere- preserving transformations of conformally closed spaces [cf. the author, Beiträge zur projektiven Inversion and deren Linearisierung (Ph. D. Thesis, TU München) (1985; Zbl 0572.51017)].