Cartan angular invariant and deformations of rank 1 symmetric spaces

Abstract

New geometric invariants in the quaternionic hyperbolic space and in the hyperbolic Cayley plane are introduced and studied. In these non-commutative and non-associative geometries they are a substitution for the Toledo invariant and the Cartan angular invariant well known in complex hyperbolic geometry. These new invariants are used for the investigation of quasi-Fuchsian deformations of quaternionic and octonionic hyperbolic manifolds. In particular, bendings are defined for such structures, which are the last two classes of locally symmetric structures of rank 1.Bibliography: 27 titles.