A 3-dimensional contact group is a 3-dimensional Lie group endowed with a left-invariant contact structure. Making use of techniques from Riemannian geometry, we prove that any simply connected 3-dimensional contact group not isomorphic to SU(2) satisfies a unique factorization property. As an application, we develop a method to construct embeddings of 3-dimensional simply connected contact groups into one among two model tight contact manifolds.
Categories: math.SG math.DG