Abstract

A classical result of Fathi and Herman from 1977 states that a smooth compact connected manifold without boundary admitting a locally free action of a 1-torus, respectively, an almost free action of a 2-torus, admits a minimal diffeomorphism, respectively, a minimal flow. In the first part of our paper we study the existence of locally free and almost free actions of tori on homogeneous spaces of compact connected Lie groups, thus providing new examples of spaces admitting minimal diffeomorphisms or flows. In the second part we combine the ideas of Fathi and Herman with our recent ideas to study the existence of minimal skew products over certain minimal flows with general connected Lie groups as acting groups. Our results apply to so called flows with free cycles. In the last part of our work we study the existence of free cycles in homogeneous flows.

中文翻译：

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平滑动态的最小扩展

摘要

Fathi 和 Herman 1977 年的经典结果指出，无边界的光滑紧连通流形分别允许 1-环面的局部自由作用、2-环面的几乎自由作用，分别允许最小微分同胚、最小流动。在本文的第一部分中，我们研究了紧连通李群的齐次空间上环面局部自由和几乎自由作用的存在性，从而提供了允许最小微分同胚或流的空间的新例子。在第二部分中，我们将 Fathi 和 Herman 的想法与我们最近的想法相结合，研究以一般连通李群作为作用群的某些最小流上最小偏斜积的存在性。我们的结果适用于所谓的自由循环流。在我们工作的最后一部分，我们研究均质流中自由循环的存在。