2022
DOI: 10.1017/etds.2022.70
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On Anosovity, divergence and bi-contact surgery

Abstract: We discuss a metric description of the divergence of a (projectively) Anosov flow in dimension 3, in terms of its associated expansion rates and give metric and contact geometric characterizations of when a projectively Anosov flow is Anosov. We then study the symmetries that the existence of an invariant volume form yields on the geometry of an Anosov flow, from various viewpoints of the theory of contact hyperbolas, Reeb dynamics, and Liouville geometry, and give characterizations of when an Anosov flow is v… Show more

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Cited by 2 publications
(3 citation statements)
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“…Therefore, X is a contact Anosov flow with constant expansion and contraction rates. It is shown by Green [24], reiterated in [17] or [31], that in this case we furthermore have [e 1 , e 2 ] = [e s , e u ] = aX for some constant a. In our case, a = 2 since g([e 1 , e 2 ], X) = 2.…”
Section: Critical Contact Metrics and The Chern-hamilton Questionmentioning
confidence: 60%
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“…Therefore, X is a contact Anosov flow with constant expansion and contraction rates. It is shown by Green [24], reiterated in [17] or [31], that in this case we furthermore have [e 1 , e 2 ] = [e s , e u ] = aX for some constant a. In our case, a = 2 since g([e 1 , e 2 ], X) = 2.…”
Section: Critical Contact Metrics and The Chern-hamilton Questionmentioning
confidence: 60%
“…In fact, it is known (see [31]) that when the flow preserves a volume form such condition implies hyperbolicity (and when satisfied globally, implies Anosovity of the flow). We will later see this explicitly in Lemma 5.3.…”
Section: Torsion Dirichlet Functional and Critical Contact Metricsmentioning
confidence: 99%
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