A theorem of non-metric rigidity for Hermitian locally symmetric manifolds

被引:11
作者
Klingler, B [1 ]
机构
[1] Ecole Polytech, Ctr Math, CNRS, UMR 7640, F-91128 Palaiseau, France
关键词
locally symmetric spaces; rigidity; projective structures; uniformization;
D O I
10.1007/s00014-001-8320-0
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let X be an irreducible Hermitian symmetric space of non-compact type of dimension greater than 1 and G be the group of biholomorphisms of X : let M = Gamma \X be a quotient of X by a torsion-free discrete subgroup Gamma of G such that M is of finite volume in the canonical metric. Then, due to the C-equivariant Borel embedding of X into its compact dual X-c, the locally symmetric structure of M can be considered as a special kind of a ( G(c), X-c) - structure on M, a maximal atlas of X-c -valued charts with locally constant transition maps in the complexified group G(C). By Mostow's rigidity theorem the locally symmetric structure of M is unique. We prove that the (G(C), X-c) -structure of M is the unique one compatible with its complex structure. In the rank one case this result is due to Mok and Yeung.
引用
收藏
页码:200 / 217
页数:18
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