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A note on Weinstein’s conjecture


Author: Augustin Banyaga
Journal: Proc. Amer. Math. Soc. 109 (1990), 855-858
MSC: Primary 58F22; Secondary 58F05, 58F18
DOI: https://doi.org/10.1090/S0002-9939-1990-1021206-0
MathSciNet review: 1021206
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Abstract: We prove that the contact foliation of a compact contact manifold $\left ( {M,\alpha } \right )$ has at least one compact leaf in the following two cases: (i) $\alpha$ is a $K$-contact form and $M$ is simply connected, (ii) $\alpha$ is ${C^2}$-close to a regular contact form. This solves the Weinstein conjecture in those particular cases.


References [Enhancements On Off] (What's this?)

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Additional Information

Keywords: <IMG WIDTH="24" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$K$">-contact form, contact foliation, Riemannian foliation, transverse symplectic structure, characteristics
Article copyright: © Copyright 1990 American Mathematical Society