Topics in Contemporary Differential Geometry, Complex by Stancho Dimiev, Kouei Sekigawa

By Stancho Dimiev, Kouei Sekigawa

This quantity comprises the contributions through the individuals within the 8 of a sequence workshops in advanced research, differential geometry and mathematical physics and comparable components. energetic experts in mathematical physics give a contribution to the quantity, delivering not just major details for researchers within the quarter but additionally attention-grabbing arithmetic for non-specialists and a broader viewers. The contributions deal with issues together with differential geometry, partial differential equations, integrable platforms and mathematical physics.

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R. Johnson, J. Fluid. Mech. 457, 63 (2002). 18. B. Khesin and G. Misiolek, Adv. Math. 176, 116 (2003). 19. A. Kirillov, Funct. Anal. Appl. 15, 135 (1981). , Contemp. Math. 145, 33 (1993). 20. April 24, 2007 17:34 WSPC - Proceedings Trim Size: 9in x 6in pcsvf2006 Camassa-Holm equation as a geodesic flow 21. 22. 23. 24. B. Kolev, J. Nonlinear Math. Phys. 11, 480 (2004). J. Lenells, J. Diff. Eq. 217, 393 (2005). G. Misiolek, J. Geom. Phys. 24, 203 (1998). E. Reyes, Lett. Math. Phys. 59, 117 (2002). 41 April 24, 2007 17:34 WSPC - Proceedings Trim Size: 9in x 6in pcsvf2006 42 FERMI-WALKER PARALLEL TRANSPORT, TIME EVOLUTION OF A SPACE CURVE AND THE ¨ SCHRODINGER EQUATION AS A MOVING CURVE R.

76, 93 (2006). 7. A. Constantin, T. Kappeler, B. Kolev and P. Topalov, On geodesic exponential maps of the Virasoro group, Ann. Global Anal. , to appear (2006). 8. A. Constantin and B. Kolev, Comment. Math. Helv. 78, 787 (2003). , J. Nonlinear Sci. 16, 109 (2006). 9. 10. A. Constantin and W. Strauss, Comm. Pure Appl. Math. 53, 603 (2000). , J. Nonlinear Sci. 12, 415 (2002). 11. 12. A. Fokas and B. Fuchssteiner, Physica D 4, 47 (1981). 13. D. Holm and J. Marsden, in The breadth of symplectic and Poisson geometry, Progr.

J. Saunders, The Geometry of Jet Bundles, Cambridge University Press, 1989. 15. S. Titcombe, L. Glass, D. Guehl and A. Beutera, Dynamics of Parkinsonian tremor during deep brain stimulation, Chaos, 11, 4 (2001), 766–773. 16. C. Udri¸ste, Geometric Dynamics, Kluwer Academic Publishers, 2000. April 24, 2007 17:34 WSPC - Proceedings Trim Size: 9in x 6in pcsvf2006 33 THE CAMASSA-HOLM EQUATION AS A GEODESIC FLOW FOR THE H 1 RIGHT-INVARIANT METRIC A. I. ie The fundamental role played by the Lie groups in mechanics, and especially by the dual space of the Lie algebra of the group and the coadjoint action are illustrated through the Camassa-Holm equation (CH).

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