We prove that any small enough neighborhood of a closed contact submanifold is always tight provided its normal bundle has a nowhere vanishing section. The non-existence of $\mathcal{C}^0$–small positive loops of contactomorphisms in general overtwisted manifolds is shown as a corollary.

中文翻译：

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接触子流形的紧密邻域

我们证明闭合接触子流形的任何足够小的邻域总是紧的，只要其正常束没有消失的部分。推论不存在$ \ mathcal {C} ^ 0 $-一般超扭曲流形中的同形小正循环。