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A note about isothermic surfaces in Rn−j,j

  • Autores: M P Dussan, M. A. Magid
  • Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 26, Nº. 2, 2008 (Ejemplar dedicado a: Revista Integración), págs. 61-76
  • Idioma: inglés
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  • Resumen
    • ABSTRACT In this note we survey our results on the description of ti-melike isothermic surfaces in Rn-j,j using the Grassmannian systems or U/K-systems. We give the natural extensions of the definition of Ribaucour and Darboux transformations for timelike isothermic surfaces and review how those transformations correspond to dressing actions of suitable simple elements.       

  • Referencias bibliográficas
    • Citas [1] A.I. Bobenko, “Surfaces in terms of 2 by 2 matrices, old and new integrable cases”,Harmonic maps and Integrable systems, Edited...
    • [2] M. Bruck, X. Du, J. Park, C-L. Terng, “The Submanifolds Geometries associatedto Grassmannian Systems”, Memoirs of A.M.S. 735 (2002).
    • [3] F. Burstall, “Isothermic surfaces: conformall geometry, Clifford algebras and Integrable systems”, Preprint, math-dg/0003096.
    • [4] F. Burstall, U. Hertrich-Jeromin, F. Pedit, U. Pinkall, “Curved flats and isothermic surfaces”, Math. Z. no. 2, 225 (1997).
    • [5] J. Ciesliski, P. Goldstein, A. Sym, “Isothermic surfaces in E3 as soliton surfaces”, Phys. Lett. A 205 (1995), 37-43.
    • [6] J. Ciesliski, “The Darboux-Bianchi transformation for isothermic surfaces”, Differential Geom. Appl. 7 (1997), 1-28.
    • [7] M. Dajczer, R. Tojeiro, “Commuting Codazzi tensors and the Ribaucour transformation
    • for submanifolds”, Results in Math. 44, (2003), 258-278.
    • [8] M.P. Dussan, M.A. Magid, “Timelike isothermic surfaces associated to Grassmannian systems”, Doc. Math. 10, (2005), 527-549.
    • [9] M.P. Dussan, M.A. Magid, “Complex Timelike isothermic surfaces and their Geometric transformations”, Balkan J. Geom. Appl. 11, (2006),...
    • [10] A. Fujioka, J. Inoguchi, “Spacelike surfaces and Harmonic Inverse Mean curvature”, J. Math. Sci. Univ. Tokyo. 7, (2000). 657-698.
    • [11] U. Hertrich-Jeromin, F. Pedit, “Remarks on the Darboux transform of isothermic surfaces”, Doc. Math. 2, (1997), 313-333.
    • [12] M.A. Magid, “Lorenztian Isothermic surfaces in Rn-j ”, Rocky Mountain J.M. 35, (2005), 627-640.
    • [13] A. Pressley, G.B. Segal, Loop Groups. Oxford Science Publ. Clarendon Press, Oxford. (1986).
    • [14] C.L. Terng, “Soliton equations and Differential Geometry”, J. Differential Geom. 45, (1997), no. 2. 407-445.
    • [15] C.L. Terng, K. Uhlenbeck, “Backlund transformations and loop group actions”, Comm. Pure Appl. Math. 53, (2000), 1-75.
    • [16] C. Tian, “Bäcklund transformation on surfaces with K = −1 in R2,1”, J. of Geom. and Phys. 22 (1997), 212-218.
    • [17] D. Zuo, Q. Chen, Y. Cheng, “Gp,qm,n-System II and diagonalizable timelike immersions in Rp,m ”, Inverse Problems, 20 (2004), 319-329.

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