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

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

2011-04-01

arxiv.org/abs/1104.0250v1

J. Topol. Anal. 3 (2011), no. 4, 405-421

Mathematics

Dynamical Systems

11 pages, 2 figures

Scientific paper

10.1142/S1793525311000684

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 $(M,\xi)$ with $\pi_2(M) \ne 0$. 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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