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

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...

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Bibliographic Details
Published in:arXiv.org 2011-04
Main Authors: Niederkrüger, Klaus, Rechtman, Ana
Format: Article
Language:English
Subjects:
Manifolds (mathematics)
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1104.0250