Topology of horocycles on geometrically finite nonpositively curved surfaces

IF 0.5 4区数学 Q3 MATHEMATICS

Geometriae Dedicata Pub Date : 2024-07-28 DOI:10.1007/s10711-024-00941-z

Sergi Burniol Clotet

引用次数: 0

Abstract

We study the closure of horocycles on rank 1 nonpositively curved surfaces with finitely generated fundamental group. Each horocycle is closed or dense on a certain subset of the unit tangent bundle. In fact, we classify each half-horocycle in terms of the associated geodesic rays. We also determine the nonwandering set of the horocyclic flow and characterize the surfaces admitting a minimal set for this flow.

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几何有限非正曲面上的角环拓扑学

我们研究具有有限生成基群的 1 级非正曲曲面上的角循环闭合。每个角循环都在单位切线束的某个子集上封闭或密集。事实上，我们根据相关的大地射线对每个半角环进行了分类。我们还确定了角环流的非漫游集，并描述了容纳该流最小集的曲面的特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Geometriae Dedicata 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Geometriae Dedicata concentrates on geometry and its relationship to topology, group theory and the theory of dynamical systems. Geometriae Dedicata aims to be a vehicle for excellent publications in geometry and related areas. Features of the journal will include: A fast turn-around time for articles. Special issues centered on specific topics. All submitted papers should include some explanation of the context of the main results. Geometriae Dedicata was founded in 1972 on the initiative of Hans Freudenthal in Utrecht, the Netherlands, who viewed geometry as a method rather than as a field. The present Board of Editors tries to continue in this spirit. The steady growth of the journal since its foundation is witness to the validity of the founder''s vision and to the success of the Editors'' mission.