Harmonic mappings and hyperbolic Plücker transformations (Q5944998)

\(\pi_h\) denotes a 3-dimensional hyperbolic space with Euclidean ground field \(K\). In this paper, the author establishes that there is a certain procedure by which any harmonic mapping of the projective line over the unique quadric extension of \(K\) induces an orthogonality-preserving Plücker transformation of \(\pi_h\) and conversely, any orthogonality-preserving Plücker transformation of \(\pi_h\) is induced by such a harmonic mapping.