Geodesic planes in geometrically finite acylindrical -manifolds
Geodesic planes in geometrically finite acylindrical -manifolds
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几何有限圆柱流形中的测地平面
DOI：
10.1017/etds.2021.19
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发表时间：
2022
影响因子：
0.9
通讯作者：
OH, HEE
中科院分区：
文献类型：
--
作者：
BENOIST, YVES;OH, HEE
设M为几何有限的非圆柱形双曲流形，并表示M的凸核的内部。我们证明了其中的任何测地线平面要么是封闭的，要么是密集的，并且在其中只有可数个封闭的测地线平面。这些结果由McMullen， Mohammadi和Oh[在双曲3-流形中的测地线平面得到。发明。数学学报。209 (2017),425-461；非圆柱形三流形凸芯中的测地线平面。杜克大学数学。[J] ., to appear, Preprint, 2018, arXiv:1802.03853]当M是凸紧时。作为推论，我们得到当M覆盖算术双曲流形时，in的测地线平面的拓扑行为受in的相应平面的拓扑行为支配。我们构造了一个非算术的反例。
Let M be a geometrically finite acylindrical hyperbolic -manifold and let denote the interior of the convex core of M. We show that any geodesic plane in is either closed or dense, and that there are only countably many closed geodesic planes in . These results were obtained by McMullen, Mohammadi and Oh [Geodesic planes in hyperbolic 3-manifolds. Invent. Math.209 (2017), 425–461; Geodesic planes in the convex core of an acylindrical 3-manifold. Duke Math. J., to appear, Preprint, 2018, arXiv:1802.03853] when M is convex cocompact. As a corollary, we obtain that when M covers an arithmetic hyperbolic -manifold , the topological behavior of a geodesic plane in is governed by that of the corresponding plane in . We construct a counterexample of this phenomenon when is non-arithmetic.