Locally symmetric spaces are generalizations of spaces of constant
curvature. In this book the author presents the proof of a remarkable
phenomenon, which he calls "strong rigidity" this is a stronger form of
the deformation rigidity that has been investigated by Selberg,
Calabi-Vesentini, Weil, Borel, and Raghunathan.
The proof combines the theory of semi-simple Lie groups, discrete
subgroups, the geometry of E. Cartan's symmetric Riemannian spaces,
elements of ergodic theory, and the fundamental theorem of projective
geometry as applied to Tit's geometries. In his proof the author
introduces two new notions having independent interest: one is
"pseudo-isometries"; the other is a notion of a quasi-conformal mapping
over the division algebra K (K equals real, complex, quaternion, or
Cayley numbers). The author attempts to make the account accessible to
readers with diverse backgrounds, and the book contains capsule
descriptions of the various theories that enter the proof.