Classification of quaternionic hyperbolic isometries

Abstract

Let F denote either the complex numbers C or the quaternions H. Let HnF denote the n-dimensional hyperbolic space over F. We obtain algebraic criteria to classify the isometries of HnF. 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 HnC is also obtained. © 2013 American Mathematical Society.