Showing papers on "Reeb vector field published in 1996"
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TL;DR: In this paper, it was shown that every Reeb vector field on Riemann surfaces has a periodic orbit which is unknotted and has self-linking number equal to 1.
Abstract: It is well known that a Reeb vector field on $S^3$
has a periodic solution. Sharpening this
result we shall show in this note that every Reeb vector field $X$
on $S^3$
has a periodic orbit which is unknotted and has self-linking
number equal to $-1$. If the contact form $\lambda$ is non-degenerate,
then there is even a periodic orbit $P$ which, in addition, has
an index $\mu (P) \in \{2,3\}$, and which spans an embedded disc whose
interior is transversal to $X$. The proofs are based on a theory for
partial differential equations of Cauchy-Riemann type for maps from
punctured Riemann surfaces into ${\mathbb R} \times S^3$, equipped with
special almost complex structures related to the contact form $\lambda$
on $S^3$.
34 citations