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Inversive closure of metric affine space and its automorphisms. (English) Zbl 0939.51001

The author considers stereographic projection from a quadric \(Q\) onto an affine space \(A\), such that orthogonality of lines in \(A\) is defined via conjugacy of their ideal points with respect to \(Q\). Conversely, for all \(A\) there is an appropriate \(Q\), and automorphisms of \(A\) are found to be induced by automorphisms of \(Q\) [cf. Theorem 4.3.7. in E. Schröder’s paper: ‘Metric geometry’, in: Buekenhout, Francis (ed.), Handbook of incidence geometry. North-Holland, 945-1013 (1995; Zbl 0826.51008)].

MSC:

51B05 General theory of nonlinear incidence geometry

Citations:

Zbl 0826.51008
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