Abstract
This paper is devoted to the study of the Landau-Lifschitz equation (LL) as the Euler equations on a current group. The current group G = G (M, SO(3)) is the configuration space of the ferromagnet magnetization problem, which is described by LL. The Lie algebra of G is the current algebra g =g(M,so(3)). It is convenient to introduce a nonstandaxd Lie bracket in g, then the geodesics of a left-invariant metric on G become the solutions of LL. The expression of the curvature tensor on G is obtained. In the case M = T 3 (the 3-torus), examples of the calculation of the sectional curvature are presented.
Mathematics subject classification (1991): 81R10, 58B25.
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Lukatsky, A.M. (1998). On The Geometry of Current Groups and a Model of The Landau-Lifschitz Equation. In: Komrakov, B.P., Krasil’shchik, I.S., Litvinov, G.L., Sossinsky, A.B. (eds) Lie Groups and Lie Algebras. Mathematics and Its Applications, vol 433. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5258-7_26
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DOI: https://doi.org/10.1007/978-94-011-5258-7_26
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