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Geodesic flow on \(\text{SO}(4)\), Kac-Moody Lie algebra and singularities in the complex \(t\)-plane. (English) Zbl 0968.35010

The author studies geometrically the Euler-Arnold equations associated to geodesic flow on \(\text{SO}(3)\) for a left-invariant diagonal metric. A Lie algebra theoretical approach based on the Konstant-Kirillov coadjoint action was given. By the asymptotic analysis, the author shows that the linearization of the Euler-Arnold equations occurs on a related Prym variety.

MSC:

35A30 Geometric theory, characteristics, transformations in context of PDEs
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