Free Access
Volume 19, Number 2, April-June 2013
Page(s) 533 - 554
Published online 21 February 2013
  1. A. Agrachev, U. Boscain and M. Sigalotti, A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds. Discrete Contin. Dyn. Syst. 20 (2008) 801–822. [CrossRef] [MathSciNet] [Google Scholar]
  2. M. Berger, Volume et rayon d’injectivité dans les variétés riemanniennes de dimension 3. Osaka J. Math. 14 (1977) 191–200. [MathSciNet] [Google Scholar]
  3. M. Berger, A panoramic view of Riemannian geometry. Springer-Verlag, Berlin (2003). [Google Scholar]
  4. G. Besson, Géodésiques des surfaces de révolution. Séminaire de Théorie Spectrale et Géométrie S9 (1991) 33–38. [Google Scholar]
  5. V.G. Boltyanskii, Sufficient conditions for optimality and the justification of the dynamic programming method. SIAM J. Control 4 (1966) 326–361. [Google Scholar]
  6. B. Bonnard and J.-B. Caillau, Metrics with equatorial singularities on the sphere. HAL preprint No. 00319299 (2008) 1–30. [Google Scholar]
  7. B. Bonnard and J.-B. Caillau, Geodesic flow of the averaged controlled Kepler equation. Forum Math. 21 (2009) 797–814. [CrossRef] [MathSciNet] [Google Scholar]
  8. B. Bonnard, J.-B. Caillau, R. Sinclair and M. Tanaka, Conjugate and cut loci of a two-sphere of revolution with application to optimal control. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26 (2009) 1081–1098. [Google Scholar]
  9. B. Bonnard, J.-B. Caillau and L. Rifford, Convexity of injectivity domains on the ellipsoid of revolution: the oblate case, C. R. Acad. Sci. Paris, Sér. I 348 (2010) 1315–1318. [CrossRef] [Google Scholar]
  10. B. Bonnard, J.-B. Caillau and O. Cots, Energy minimization in two-level dissipative quantum control: the integrable case. Proc. of 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Dresden (2010). Discrete Contin. Dyn. Syst. suppl. (2011) 229–239. [Google Scholar]
  11. B. Bonnard, G. Charlot, R. Ghezzi and G. Janin, The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry. J. Dyn. Control Syst. 17 (2011) 141–161. [CrossRef] [MathSciNet] [Google Scholar]
  12. B. Bonnard, O. Cots and N. Shcherbakova, Energy minimization problem in two-level dissipative quantum systems. J. Math. Sci. 147 (2012). [Google Scholar]
  13. J.-B. Caillau, B. Daoud and J. Gergaud, On some Riemannian aspects of two and three-body controlled problems. Recent Advances in Optimization and its Applications in Engineering. Springer (2010) 205–224. Proc. of the 14th Belgium-Franco-German conference on Optimization, Leuven (2009). [Google Scholar]
  14. A. Faridi and E. Schucking, Geodesics and deformed spheres. Proc. Amer. Math. Soc. 100 (1987) 522–525. [CrossRef] [MathSciNet] [Google Scholar]
  15. A. Figalli, L. Rifford and C. Villani, Nearly round spheres look convex. Amer. J. Math. 134 (2012) 109–139. [CrossRef] [MathSciNet] [Google Scholar]
  16. G.-H. Halphen, Traité des fonctions elliptiques et de leurs applications. Première partie, Gauthier-Villars (1886). [Google Scholar]
  17. J. Itoh and K. Kiyohara, The cut loci and the conjugate loci on ellipsoids. Manuscripta Math. 114 (2004) 247–264. [CrossRef] [MathSciNet] [Google Scholar]
  18. G. Janin, Contrôle optimal et applications au transfert d’orbite et à la géométrie presque Riemannienne. Ph.D. thesis, Université de Bourgogne (2010). [Google Scholar]
  19. D. Lawden, Elliptic functions and applications. Springer-Verlag (1989). [Google Scholar]
  20. S.B. Myers, Connections between differential geometry and topology I. Simply connected surfaces II. Duke Math. J. 1 (1935) 376–391; 2 (1936) 95–102. [CrossRef] [MathSciNet] [Google Scholar]
  21. H. Poincaré, Sur les lignes géodésiques des surfaces convexes. Trans. Amer. Math. Soc. 6 (1905) 237–274. [MathSciNet] [Google Scholar]
  22. K. Shiohama, T. Shioya and M. Tanaka, The geometry of total curvature on complete open surfaces. Cambridge University Press (2003). [Google Scholar]
  23. R. Sinclair and M. Tanaka, The cut locus of a two-sphere of revolution and Toponogov’s comparison theorem. Tohoku Math. J. 59 (2007) 379–399. [CrossRef] [MathSciNet] [Google Scholar]
  24. M. Spivak, A comprehensive introduction to differential geometry II. Publish or Perish (1979). [Google Scholar]
  25. C. Villani, Optimal transport, Old and new. Springer-Verlag (2009). [Google Scholar]

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