An infinite family of hyperbolic 3-manifolds without tight projectively Anosov flows

TL;DR

This paper constructs an infinite family of hyperbolic 3-manifolds that admit tight contact structures but lack tight projectively Anosov flows, expanding understanding of contact geometry and Anosov flows in 3-manifolds.

Contribution

It introduces the first infinite family of hyperbolic 3-manifolds with tight contact structures but no tight projectively Anosov flows, obtained via rational surgeries on the figure eight knot.

Findings

Existence of hyperbolic 3-manifolds with tight contact structures but no tight projectively Anosov flows

Construction of these manifolds through rational surgeries on the figure eight knot

First such infinite family discovered in this context

Abstract

In this paper we find the first infinite family of hyperbolic 3-manifolds which admit tight contact structures but do not have any tight projectively Anosov flow. These manifolds are obtained as rational surgeries on the figure eight knot.