Transformations preserving null line sections of a domain: The arbitrary signature case (Q1071262)

The author proves the following theorem: Let V be a real metric vector space of signature (p,q), with p,q\(\geq 2\), and D be an open connected subset in V. Let \(f: D\to V\) be an injective function such that for all a,b,c in D, i) if a,b,c lie on a null line, then so do f(a), f(b) and f(c), ii) if f(a) and f(b) lie on a null line, then so do a and b. Then f is the restriction to D of a conformal transformation of V, or possibly (if \(p=q)\) of a pseudo-conformal transformation of V. The Minkowskian case of this theorem is the classical theorem of Alexandrov-Ovchinnikova.