Invariant subsets of rank 1 manifolds
Invariant subsets of rank 1 manifolds
复制标题
1 阶流形的不变子集
DOI：
10.1007/s002290100225
复制
发表时间：
2002
影响因子：
0.6
通讯作者：
V. Schroeder
中科院分区：
文献类型：
--
作者：
S. Buyalo;V. Schroeder
摘要：证明了对于具有非正截面曲率和有限体积的黎曼流形 M，测地射线避开固定秩 1 向量 v∈UM 的足够小的邻域的每个点的方向空间看起来非常像广义的谢尔宾斯基地毯。我们还证明，对于暗淡 M≥ 3 的非正曲流形 M，存在单位切丛 UM 的真闭流不变子集，其足点投影是 M 的整体。
Abstract: It is proved that for a Riemannian manifold M with nonpositive sectional curvature and finite volume the space of directions at each point in which geodesic rays avoid a sufficiently small neighborhood of a fixed rank 1 vector v∈UM looks very much like a generalized Sierpinski carpet. We also show for nonpositively curved manifolds M with dim M≥ 3 the existence of proper closed flow invariant subsets of the unit tangent bundle UM whose footpoint projection is the whole of M.