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arXiv · 1104.0250

The Weinstein conjecture in the presence of submanifolds having a Legendrian foliation

Klaus Niederkrüger·Ana Rechtman
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Abstract

Helmut Hofer introduced in '93 a novel technique based on holomorphic curves to prove the Weinstein conjecture. Among the cases where these methods apply are all contact 3--manifolds $(M,ξ)$ with $π_2(M) \ne 0$. We modify Hofer's argument to prove the Weinstein conjecture for some examples of higher dimensional contact manifolds. In particular, we are able to show that the connected sum with a real projective space always has a closed contractible Reeb orbit.

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Klaus Niederkrüger, Ana Rechtman. 2011-04-01. The Weinstein conjecture in the presence of submanifolds having a Legendrian foliation. https://doi.org/10.1142/s1793525311000684

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