Geodesic
Integral Formula for a Generalized Sato--Levine Invariant in Magnetic Hydrodynamics
Matematičeskie zametki, Tome 85 (2009) no. 4, pp. 524-537.

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For a pair of divergence-free vector fields $\mathbf B$ and $\widetilde{\mathbf B}$ respectively localized in two oriented tubes $U$ and $\widetilde U$ in $\mathbb R^3$, we propose a fourth-order integral $W$ and describe the dependence between the integral $W$ and a higher topological invariant $\beta=\beta(l,\widetilde l)$ (namely, the generalized Sato–Levine invariant). The new integral is a generalization of the well-known integral, which was defined earlier for two tubes with zero linking number.
Keywords: topological invariant, oriented magnetic tube, linking number, magnetic hydrodynamics, Lie derivative, Massey product, gradient field.
Mots-clés : Sato–Levine invariant 
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P. M. Akhmet'ev; O. V. Kunakovskaya. Integral Formula for a Generalized Sato--Levine Invariant in Magnetic Hydrodynamics. Matematičeskie zametki, Tome 85 (2009) no. 4, pp. 524-537. http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a3/

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