Geometriae Dedicata

, Volume 132, Issue 1, pp 105–119 | Cite as

A dynamical characterization of contact circles

  • Jesús Gonzalo Pérez
Original Paper


A simple dynamical condition is given for line fields within a contact structure, which is satisfied exactly by those line fields which are common kernels of contact circles. Some convexity properties are established which are useful in the study of contact circles up to homotopy. A necessary condition for extending a contact form to a contact circle is given. Based on work of Lisca–Matić and Honda, concrete examples are given which show that the condition is not just homotopic but a geometric one. The paper ends with an open question.


Contact structure Contact circle Flows Tightness 

Mathematics Subject Classification (2000)

53D35 57R17 57R57 37D30 


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© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Universidad Autónoma de MadridMadridSpain

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