Hyperbolic manifolds with convex boundary
Hyperbolic manifolds with convex boundary
复制标题
具有凸边界的双曲流形
DOI：
10.1007/s00222-005-0456-x
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发表时间：
2002
影响因子：
3.1
通讯作者：
Jean
中科院分区：
文献类型：
--
作者：
Jean
设（M，M）是一个3-流形，它带有一个具有凸边界的双曲度量.我们考虑M上的双曲度量，使得边界光滑且严格凸。我们证明了边界上的诱导度规恰好是曲率K>-1的度规，并且M的第三基本形式恰好是曲率K<1的度规，对于这些度规，M中可收缩的闭测地线的长度L>2π.其他的相关结果描述了其他边界条件的存在性和唯一性，当度量上实现的CNOM是一个线性组合的第一，第二和第三基本形式。
Let (M,∂M) be a 3-manifold, which carries a hyperbolic metric with convex boundary. We consider the hyperbolic metrics on M such that the boundary is smooth and strictly convex. We show that the induced metrics on the boundary are exactly the metrics with curvature K>-1, and that the third fundamental forms of ∂M are exactly the metrics with curvature K<1, for which the closed geodesics which are contractible in M have length L>2π. Each is obtained exactly once.Other related results describe existence and uniqueness properties for other boundary conditions, when the metric which is achieved on ∂M is a linear combination of the first, second and third fundamental forms.