Hyperbolic manifolds (Q2776345)

This is a short survey of the theory of hyperbolic manifolds. It starts with two pages of a brief history of hyperbolic manifolds and about two pages survey of hyperbolic 3-manifolds. The rest of the paper (and its primary emphasis) is devoted to the author's recent results (published elsewhere) on 4-dimensional hyperbolic manifolds and geometrical finiteness. Very close to these results are recent results by \textit{Dubravko Ivanšić} [Differ. Geom. Appl. 10, No. 3, 205-223 (1999; Zbl 0945.51009); Embeddability of noncompact hyperbolic manifolds as complements of codimension-1 and -2 submanifolds, Topology Appl. 120, 211-236 (2002); Hyperbolic structure on complements of tori in the 4-sphere, Preprint, George Washington Univ. (2001)], and the reviewer's book [Conformal geometry of discrete groups and manifolds, de Gruyter Expo. Math. 33 (2000; Zbl 0965.57001)].NEWLINENEWLINEFor the entire collection see [Zbl 0977.00029].