The problem of calculating of the global invariants for the action of the group of contact diffeomorphisms on itself by conjugations. The integral invariant for this action is obtained. This invariant is the analog of the Calabi invariant for the groups of symplectomorphisms of the unit disk. We normalize Cartan form for a given contact diffeomorphism and then consider the volume form on our compact manifold. This volume form is constructed with the help of the normalized Cartan form. The volume of our manifold with respect to this form is our intergal invariant.

中文翻译：

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关于接触积分卡拉比不变量

通过共轭计算接触不定形群对自身的作用的全局不变量的问题。获得该动作的积分不变式。这个不变量是单位圆盘的辛同态群的Calabi不变量的类似物。我们针对给定的接触微分定理对Cartan形式进行归一化，然后考虑紧凑流形上的体积形式。该体积形式是在归一化的Cartan形式的帮助下构建的。相对于这种形式，我们的流形的体积是我们的星际不变性。