On the integrability of geodesic flows of submersion metrics

Letters in Mathematical Physics

Volumn 61, Issue 1, 2002, Pages 29-39

  Jovanović, Božidar ^a  

^a MATHEMATICAL INSTITUTE   (Serbia)

Author keywords

Integrable geodesic flows; Noncommutative integrability; Symplectic reduction

Indexed keywords

EID: 0042315360     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020234130071     Document Type: Article

References (27)

1. Bazaikin, Ya. V.: Double quotients of Lie groups with an integrable geodesic flows, Sibirsk. Mat. Zh. 41(3) (2000), 513-530 (Russian); English translation: Siberian Math. J. 41(3) (2000), 419-432.
2. Bazaikin, Ya. V.: Double quotients of Lie groups with an integrable geodesic flows, Sibirsk. Mat. Zh. 41(3) (2000), 513-530 (Russian); English translation: Siberian Math. J. 41(3) (2000), 419-432.
3. Bogoyavlenkij, O. I.: Theory of tensor invariants of integrable Hamiltonian systems. II. Theorem on symmetries and its applications, Comm. Math. Phys. 184 (1997), 301-365.
4. Bolsinov, A. V. and Taimanov, I. A.: Integrable geodesic flow with positive topological entropy, Invent. Math. 140 (2000), 639-650.
5. Bolsinov, A. V. and Taimanov, I. A.: Integrable geodesic flows on the suspensions of toric automorphisms, Tr. Mat. Inst. Steklova 231 (2000), 46-63 (Russian); English translation: Proc. Steklov. Inst. Math. 231(4) (2000), 42-58.
6. Bolsinov, A. V. and Taimanov, I. A.: Integrable geodesic flows on the suspensions of toric automorphisms, Tr. Mat. Inst. Steklova 231 (2000), 46-63 (Russian); English translation: Proc. Steklov. Inst. Math. 231(4) (2000), 42-58.
7. Bolsinov, A. V. and Jovanović, B.: Integrable geodesic flows on homogeneous spaces, Mat. Sb. 192(7) (2001), 21-40 (Russian); English translation: Sb. Mat. 192(7-8) (2001), 951-968.
8. Bolsinov, A. V. and Jovanović, B.: Integrable geodesic flows on homogeneous spaces, Mat. Sb. 192(7) (2001), 21-40 (Russian); English translation: Sb. Mat. 192(7-8) (2001), 951-968.
9. Bolsinov, A. V. and Jovanović, B.: Non-commutative integrability, moment map and geodesic flows, to appear in Ann. Global Anal. Geom. arXiv: math-ph/0109031.
10. Brailov, A. V.: Some cases of complete integrability of the Euler equations and applications, Dokl. Akad. Nauk SSSR 268 (1983), 1043-1046 (Russian); English translation: Soviet Math. Dokl. 27 (1983), 209-212.
11. Brailov, A. V.: Some cases of complete integrability of the Euler equations and applications, Dokl. Akad. Nauk SSSR 268 (1983), 1043-1046 (Russian); English translation: Soviet Math. Dokl. 27 (1983), 209-212.
12. Eschenburg, J. H.: New examples of manifolds with strictly positive curvature, Invent. Math. 66 (1982), 469-480.
13. Gromoll, D. and Meyer, W.: An exotic sphere with nonnegative sectional curvature, Ann. Math. 100 (1974), 401-406.
14. Kozlov, V. V.: Integrability and non-integrability in Hamiltonian mechanics, Uspekhi Mat. Nauk. 38(1) (1983), 3-67 (Russian); English translation: Russian Math. Surveys 38(1) (1983), 1-76.
15. Kozlov, V. V.: Integrability and non-integrability in Hamiltonian mechanics, Uspekhi Mat. Nauk. 38(1) (1983), 3-67 (Russian); English translation: Russian Math. Surveys 38(1) (1983), 1-76.
16. Mishchenko, A. S. and Fomenko, A. T.: Generalized Liouville method of integration of Hamiltonian systems, Funktsional. Anal. i Prilozhen. 12(2) (1978), 46-56 (Russian); English translation: Funct. Anal. Appl. 12 (1978), 113-121.
17. Mishchenko, A. S. and Fomenko, A. T.: Generalized Liouville method of integration of Hamiltonian systems, Funktsional. Anal. i Prilozhen. 12(2) (1978), 46-56 (Russian); English translation: Funct. Anal. Appl. 12 (1978), 113-121.
18. Nekhoroshev, N. N.: Action-angle variables and their generalization, Tr. Mosk. Mat. Obs. 26 (1972), 181-198, (Russian); English translation: Trans. Moscow Math. Soc. 26 (1972), 180-198.
19. Nekhoroshev, N. N.: Action-angle variables and their generalization, Tr. Mosk. Mat. Obs. 26 (1972), 181-198, (Russian); English translation: Trans. Moscow Math. Soc. 26 (1972), 180-198.
20. Paternain, G. P.: On the topology of manifolds with completely integrable geodesic flows I, II, Ergodic Theory Dynam. Systems 12 (1992), 109-121; J. Geom. Phys. 13 (1994), 289-298.
21. Paternain, G. P.: On the topology of manifolds with completely integrable geodesic flows I, II, Ergodic Theory Dynam. Systems 12 (1992), 109-121; J. Geom. Phys. 13 (1994), 289-298.
22. Paternain, G. P. and Spatzier, R. J.: New examples of manifolds with completely integrable geodesic flows, Adv. in Math. 108 (1994), 346-366.
23. Taimanov, I. A.: The topology of Riemannian manifolds with integrable geodesic flows, Trudy Mat. Inst. Steklova 205 (1994), 150-164 (Russian); English translation: Proc. Steklov. Inst. Math. 205(4) (1995), 139-150.
24. Taimanov, I. A.: The topology of Riemannian manifolds with integrable geodesic flows, Trudy Mat. Inst. Steklova 205 (1994), 150-164 (Russian); English translation: Proc. Steklov. Inst. Math. 205(4) (1995), 139-150.
25. Thimm, A.: Integrable geodesic flows on homogeneous spaces, Ergodic Theory Dynam. Systems 1 (1981), 495-517.
26. Trofimov, V. V. and Fomenko, A. T.: Geometric and algebraic mechanisms of the integrability of Hamiltonian systems on homogeneous spaces and Lie algebras, In: V. I. Arnold and S. P. Novikov (eds), Dynamical Systems VII, Springer, New York, 1994.
27. Zung, N. T.: Reduction and integrability, arXiv: math.DS/0201087.