伪黎曼双曲空间中的凸余紧性
Convex cocompactness in pseudo-Riemannian hyperbolic spaces
摘要：
字双曲群到高秩半单李群的Anosov表示是具有有限核和离散象的表示，它与凸余紧表示到秩一李群有很强的相似性。然而，最天真的类比失败了：一般来说，Anosov表示不正确地作用于相关黎曼对称空间中的凸集上。研究了投射不定正交群PO（p，q）在伪黎曼双曲空间H^{p，q-1}上的作用，以代替黎曼对称空间.根据Barbot和Mérigot在反德西特几何中的工作，我们发现Anosov表示与凸余紧性的自然概念之间存在密切联系。
英文摘要：
Anosov representations of word hyperbolic groups into higher-rank semisimple Lie groups are representations with finite kernel and discrete image that have strong analogies with convex cocompact representations into rank-one Lie groups. However, the most naive analogy fails: generically, Anosov representations do not act properly and cocompactly on a convex set in the associated Riemannian symmetric space. We study representations into projective indefinite orthogonal groups PO(p,q) by considering their action on the associated pseudo-Riemannian hyperbolic space H^{p,q-1} in place of the Riemannian symmetric space. Following work of Barbot and Mérigot in anti-de Sitter geometry, we find an intimate connection between Anosov representations and the natural notion of convex cocompactness in this setting.
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