Enciso Alberto, Peralta-Salas Daniel, de Lizaur Francisco Torres
Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, 28049 Madrid, Spain
Proc Natl Acad Sci U S A. 2016 Feb 23;113(8):2035-40. doi: 10.1073/pnas.1516213113. Epub 2016 Feb 10.
We prove that any regular integral invariant of volume-preserving transformations is equivalent to the helicity. Specifically, given a functional I defined on exact divergence-free vector fields of class C(1) on a compact 3-manifold that is associated with a well-behaved integral kernel, we prove that I is invariant under arbitrary volume-preserving diffeomorphisms if and only if it is a function of the helicity.
我们证明，保体积变换的任何正则积分不变量都与螺旋度等价。具体而言，给定一个定义在紧致三维流形上(C(1))类的精确无散向量场上的泛函(I)，它与一个表现良好的积分核相关联，我们证明，当且仅当(I)是螺旋度的函数时，(I)在任意保体积微分同胚下是不变的。
