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    Title      l  The contact sphere theorem in dimension three
    Author   l  Jin Hong Kim
    Date   l  2013-04-30
    Category   l  ASARC-Prepint-13-02
    Download    l 1391654941_0.173399.pdf  
Given a closed contact three-manifold with a compatible Riemannian
metric g, in this paper we show that if the Ricci curvature Ric(g) of g is
positive, then the contact structure is universally tight. This result can be
thought of as a three-dimensional contact version of the well-known sphere
theorem in Riemannian geometry, and affirmatively answers a question in
Invent. Math. posed by Etnyre, Komendarczyk, and Massot. The basic idea
of the proof of main result is to make use of the one-parameter family of
Riemannian metrics obtained by the Hamilton’s Ricci flows and their corresponding
family of contact one-forms.

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