On Anosovity, divergence and bi-contact surgery

Surena Hozoori

Published 2021-09-01Version 1

We discuss a metric description of the divergence of a (projectively) Anosov flow in dimension 3, in terms of its associated growth rates and give metric and contact geometric characterizations of when a projectively Anosov flow is Anosov. As an application, we show that, in the case of volume preserving flows, the bi-contact surgery operations of Salmoiraghi can be applied in any arbitrary small neighborhood of a periodic orbit of such flows. In particular, for volume preserving Anosov flows, the Goodman-Fried's surgery can be performed, using bi-contact surgery. We also give the first examples of taut contact hyperbolas on hyperbolic manifolds, as well as a Reeb dynamical characterization of when a (projectively) Anosov is volume preserving.