Integral formula for a generalized Sato-Levine invariant in magnetic hydrodynamics
The authors investigate the problem of finding a higher analog of the helicity integral for divergence-free vector fields. They propose the construction of a new fourth-order integral \(\mathbf{W}\) which is defined for the magnetic field represented by two tubes, and extend a previous integral defined for two tubes with zero linking number [J. Geom. Phys. 15, No.~2, 95--101 (1995; Zbl 0836.57005)]. It is shown that \(\mathbf{W}\) is preserved under the motion of tubes in an ideal medium. Also, the topological meaning of \(\mathbf{W}\) is discussed and compared with the generalized Sato-Levine invariant.
scientific article; zbMATH DE number 5628180