A Proof On Arnold Chord Conjecture

Details A Proof On Arnold Chord Conjecture A Proof On Arnold Chord Conjecture

2009-01-18

arxiv.org/abs/0901.2440v3

Mathematics

General Mathematics

This paper contains a gap. This submission has been withdrawn by the author.

Scientific paper

In this article, we first prove that there exists a smooth foliation near codimension one skeleton which is transversal to the Reeb vector field on the contact manifold. Second, we use it to prove that there exists a smooth Poincare section for the Legendre submanifold. Third, we give a proof on the Arnold chord conjecture which states that every Reeb flow has at least as many Reeb chords as a smooth function on the Legendre submanifold has critical points. This also implies a proof on the fact that there exists at least one close Reeb orbits on any close contact manifold.

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