New Classes of Quasigeodesic Anosov Flows in $3$-Manifolds

Abstract

Quasigeodesic behavior of flow lines is a very useful property in the study of Anosov flows. Not every Anosov flow in dimension three is quasigeodesic. In fact up to orbit equivalence, the only previously known examples of quasigeodesic Anosov flows were suspension flows. In this article, we prove that a new class of examples are quasigeodesic. These are the first examples of quasigeodesic Anosov flows on three manifolds that are neither Seifert, nor solvable, nor hyperbolic. In general, it is very hard to show that a given flow in quasigeodesic, and in this article we provide a new method to prove that an Anosov flow is quasigeodesic.