Isometry Group Of Complex Hyperbolic Manifolds

The main purpose of this thesis is to investigate the discreteness of normalizerof the isometric groups of geometric finite complex hyperbolic manifolds and theparameterizing of complex hyperbolic triangle groups.At first, by discussing the discreteness of normalizer of isometric group, weobtain that the isometric group of geometric finite complex hyperbolic manifoldis finite if and only if the normalizer is discrete. Then, using the above result, weknow that the isometric group of compact complex hyperbolic manifold is finite,and give new and brief proofs of the two Ratcli?e's theorems.At last, we get a parameterizing theorem of (p1,l2,p3) triangle groups andstudy the space of (p1,l2,p3) triangle groups by the angular invariant.