Classification of quaternionic hyperbolic isometries

Abstract

Let F denote either the complex numbers C or the quaternions H. Let Hn F denote the n-dimensional hyperbolic space over F. We obtain algebraic criteria to classify the isometries of Hn F . This generalizes the work in Geom. Dedicata 157 (2012), 23–39 and Proc. Amer. Math. Soc. 141 (2013), 1017– 1027, to isometries of arbitrary dimensional quaternionic hyperbolic space. As a corollary, a characterization of isometries of Hn C is also obtained.