Remarks on the horocycle flows for foliations by hyperbolic surfaces

TL;DR

This paper investigates the dynamics of horocycle flows on foliated hyperbolic surfaces, establishing conditions under which these flows are minimal, thus contributing to the understanding of their long-term behavior.

Contribution

It provides new criteria for the minimality of horocycle flows in the context of foliations by hyperbolic surfaces, extending previous results in the field.

Findings

Horocycle flow is minimal under certain conditions.

Conditions for minimality depend on foliation properties.

Enhances understanding of flow dynamics on hyperbolic surface foliations.

Abstract

We show that the horocycle flow associated with a foliation on a compact manifold by hyperbolic surfaces is minimal under certain conditions.