Maximal volume representations are Fuchsian

被引：19

作者：

Francaviglia, S ^{[1
]}

Klaff, B

机构：

[1] Univ Autonoma Barcelona, E-08193 Barcelona, Spain

[2] Univ Texas, Austin, TX 78712 USA

来源：

GEOMETRIAE DEDICATA | 2006年 / 117卷 / 01期

关键词：

hyperbolic geometry; rigidity; natural maps;

D O I：

10.1007/s10711-005-9033-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a volume- rigidity theorem for Fuchsian representations of fundamental groups of hyperbolic k- manifolds into Isom(H-n). Namely, we show that if M is a complete hyperbolic k- manifold with finite volume, then the volume of any representation of pi(1)(M) into Isom(H-n), 3 <= k <= n, is less than the volume of M, and the volume is maximal if and only if the representation is discrete, faithful and `k- Fuchsian'.

引用

页码：111 / 124

页数：14

共 12 条

[1]

Benedetti R., 1992, LECT HYPERBOLIC GEOM

[2] Real Schwartz lemma and geometric applications [J].