Relative and absolute differential invariants for conformal curves

Journal of Lie Theory

Volumn 13, Issue 1, 2003, Pages 213-245

  Beffa, Gloria Marí ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22544455147     PISSN: 09495932     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. Ackerman, M., and R. Hermann, "Sophus Lie's 1884 Differential Invariant Paper," Math. Sci. Press, Brookline, Mass., 1975.
2. Cartan, E., La Méthode du Repère Mobile, la Théorie des Groupes Continus et les Espaces Généralisés, "Exposés de Géométrie" 5, Hermann, Paris, 1935.
3. Cartan, E., La Théorie des Groupes Finis et Continus et la Géométrie Différentielle Traitées par la Méthode du Repère Mobile, "Cahiers Scientifiques", 18, Gauthier-Villars, Paris, 1937.
4. Fels, M., and P. Olver, Moving coframes. I. A practical algorithm, Acta Appl. Math. 51 (1998), 161-213.
5. _, Moving coframes. II. Regularization and theoretical foundations, Acta Appl. Math. 55 (1999), 127-208.
6. Fialkow, A., The Conformal Theory of Curves, "Transactions of the AMS" 51 (1942), 435-568.
7. González-López, A., R. Heredefo, and G. Marí Beffa, Invariant differential equations and the Adler-Gel'fand-Dikii bracket, J. Math. Phys. 38 (1997), 5720-5738.
8. Guillemin V. and S. Sternberg, Variations on a theme by Kepler, "Colloquium publ. Amer. Math. Soc." 42, Providence R. I. 1990.
9. Green, Mark L. A., The moving frame, differential invariants, and rigidity theorems for curves in homogeneous spaces, Duke Math. J. 45 (1978), 735-779.
10. Hasimoto, R., A soliton on a vortex filament, J. Fluid Mechanics 51 (1972), 477-485.
11. Ivey, T. A., Integrable geometric evolution equations for curves, Technical report (2001), to be published in Contemporary Mathematics.
12. Langer, J., and R. Perline, Poisson geometry of the filament equation, J. Nonlinear Sci. 1:1 (1991), 71-93.
13. Kobayashi, S., "Transformation Groups in Differential Geometry," Classics in Mathematics, Springer-Verlag, New York, 1972.
14. Lie, S., Über Differentialinvarianten, "Gesammelte Abhandlungen" 6, B. G. Teubner, Leipzig 1927; see [1] for an English translation.
15. Marí Beffa, G., The Theory of Differential Invariants and KdV Hamiltonian Evolutions, Bull. Soc. Math. France 127 (1999), 363-391.
16. _, Conformal Analogue of the Adler-Gel'fand-Dikii bracket in two dimensions, J. Phys. A: Math. Gen. 33 (2000), 4689-4707; and Corrigenda, 33 (2000), 8601.
17. _, The theory of differential invariance and infinite dimensional Hamiltonian evolutions, "Poisson geometry" (Warsaw, 1998), Polish Acad. Sci., Warsaw (2000), 187-196.
18. Mari Beffa, G., and P. Olver, Differential Invariants for parametrized projective surfaces, Comm. in Anal. and Geom. 7-4 (1999), 807-839.
19. Mari Beffa, G., J. Sanders, and J. P. Wang, Integrable systems in 3-dimensional Riemannian geometry, to appear in J. Nonlinear Sci.
20. Marsden, J., and A. Weinstein, Coadjoint orbits, vortices, and Clebsch variables for incompressible fluids, Physica D 7(1-3) (1983), 305-323.
21. Olver, P. J., "Equivalence, Invariance and Symmetry", Cambridge University Press, Cambridge, UK (1995).
22. Olver, P., G. Sapiro, and A. Tannenbaum, Differential invariant signatures and flows in computer vision: a symmetry group approach, "Geometry Driven Diffusion in Computer Vision," B. M. ter Haar Romeny, ed. Kluwer Acad. Publ., Dordrecht, The Netherlands 1994.
23. Sharpe, R. W., "Differential Geometry: Cartan's Generalization of Klein's Erlangen Program," Graduate Texts in Mathematics, Springer 1997.
24. Tresse, A., Sur les invariants différentiels des groupes continus de transformations, Acta Math. 18 (1894), 1-88.
25. Wilczynski, E. J., "Projective differential geometry of curves and ruled surfaces", B. G. Teubner, Leipzig 1906.
26. Witten, E., Coadjoint orbits of the Virasoro group, Comm. Math. Phys. 114 (1988), 1-53.
27. Zakharov, V. E., Description of the n-orthogonal curvilinear coordinate systems and Hamiltonian integrable systems of hydrodynamic type. I. Integration of the Lamé equations, Duke Math. J. 94(1) (1998), 103-139