A very important theorem in the geometry of contact manifolds, and the start of the modern theory, is the Boothby–Wang theorem, which states that a compact regular contact manifold is a principal circle bundle over a symplectic manifold of integral class. We will prove this result in Section 3.3. In preparation for this we review principal circle bundles in this chapter.
KeywordsShort Exact Sequence Symplectic Manifold Principal Bundle Connection Form Contact Manifold
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