Differentiable Family of Contact Structures on a Non-Compact (2n-1)-Manifold

Norihiko OKUBO
2002 Interdisciplinary Information Sciences  
We construct a differentiable family of non-contactomorphic contact structures on a non-compact ð2n À 1Þdimensional manifold. This generalizes a result of Eliashberg which shows the existence of non-contactomorphic open solid tori. P' à ð½zÞ ¼ ½' à ðzÞ: Then we have the following proposition from Proposition 3.2. Proposition 3.3. I c ððV " 0 0 ; 0 Þ j T n ; i " à ðÈj V " Þ Ã Þ ¼ P' à ðI c ððV " 0 0 ; 0 Þ j T n ; i " 0 0 à ÞÞ: Proof. Since the map ' of Proposition 3.2 (3) is a diffeomorphism, we
more » ... diffeomorphism, we have And, noting that i " Projectivizing the result we get
doi:10.4036/iis.2002.177 fatcat:hjf575zwvfdopfevyw3jtwdu4y