Geodesic flow on \(SO(4)\) and Abelian surfaces. (English) Zbl 0521.58042


37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53D25 Geodesic flows in symplectic geometry and contact geometry
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
14K10 Algebraic moduli of abelian varieties, classification
17B45 Lie algebras of linear algebraic groups
Full Text: DOI EuDML


[1] Adler, M., van Moerbeke, P.: Completely integrable systems. Euclidean Lie algebras and curves. Adv. Math.38, 267-317 (1980) · Zbl 0455.58017 · doi:10.1016/0001-8708(80)90007-9
[2] Adler, M., van Moerbeke, P.: Linearization of Hamiltonian systems, Jacobi varieties and representation theory. Adv. Math.38, 318-379 (1980) · Zbl 0455.58010 · doi:10.1016/0001-8708(80)90008-0
[3] Adler, M., van Moerbeke, P.: Kowalewski’s asymptotic method. Kac-Moody Lie algebras and regularization. Commun. Math. Phys.83, 83-106 (1982) · Zbl 0491.58017 · doi:10.1007/BF01947073
[4] Adler, M., van Moerbeke, P.: The algebraic integrability of geodesic flow on SO(4). Invent. Math.67, 297-331 (1982) · Zbl 0539.58012 · doi:10.1007/BF01393820
[5] Mumford, D.: Appendix to [4]
[6] Dikii, L.A.: Hamiltonian systems connected with the rotation group. Funct. Anal. Appl.6, 83-84 (1972)
[7] Griffiths, P., Harris, J.: Principles of algebraic geometry. New York: Wiley-Interscience 1978 · Zbl 0408.14001
[8] Knörrer, H.: Geodesics on the ellipsoid. Invent. Math.59, 119-144 (1980) · Zbl 0431.53003 · doi:10.1007/BF01390041
[9] Kowalewski, S.: Sur le problème de la rotation d’un corps solide autour d’un point fixe. Acta Math.12, 177-232 (1889) · JFM 21.0935.01 · doi:10.1007/BF02592182
[10] Kowalewski, S.: Sur une propriété du système d’équations différentielles qui définit la rotation d’un corps solide autour d’un point fixe. Acta Math.14, 81-83 (1889) · JFM 22.0921.02 · doi:10.1007/BF02413316
[11] Manakov, S.V.: Remarks on the integrals of the Euler equations of then-dimensional heavy top. Funct. Anal. Appl.10, 93-94 (1976)
[12] Mischenko, A.S., Fomenko, A.T.: Luler’s equation on finite dimensional Lie groups. Math. USSR Izv.12, 371-389 (1978) · Zbl 0405.58031 · doi:10.1070/IM1978v012n02ABEH001859
[13] Moser, J.: Geometry of quadrics and spectral theory. In: The Chern Symposium 1979, pp. 147-188. Berlin, Heidelberg, New York: Springer 1980
[14] Mumford, D.: Abelian varieties. Bombay. Oxford: Oxford University Press 1974 · Zbl 0326.14012
[15] Ratiu, T.: The motion of the freen-dimensional rigid body. Indiana Univ. Math. J.29, 609-629 (1980) · Zbl 0432.70011 · doi:10.1512/iumj.1980.29.29046
[16] Reid, M.: The complete intersection of two or more quadrics. Thesis. Cambridge Univ. 1972
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