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http://dx.doi.org/10.4134/JKMS.2008.45.6.1577

RIBAUCOUR TRANSFORMATIONS ON LORENTZIAN SPACE FORMS IN LORENTZIAN SPACE FORMS  

Park, Joon-Sang (DEPARTMENT OF MATHEMATICS DONGGUK UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.6, 2008 , pp. 1577-1590 More about this Journal
Abstract
We study Ribaucour transformations on nondegenerate local isometric immersions of Lorentzian space forms into Lorentzian space forms with the same sectional curvatures which have flat normal bundles. They can be associated to dressing actions on the solution space of Lorentzian Grassmannian systems.
Keywords
Lorentzian space form; Ribaucour transformation; flat connection; nondegenerate; Lorentzian Grassmannian system;
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1 M. Bruck, X. Du, J. Park, and C. L. Terng, The submanifold geometries associated to Grassmannian systems, Mem. Amer. Math. Soc. 155 (2002), no. 735, viii+95 pp.
2 M. Dajczer and R. Tojeiro, An extension of the classical Ribaucour transformation, Proc. London Math. Soc. (3) 85 (2002), no. 1, 211-232   DOI
3 L. P. Eisenhart, A Treatise on The Differential Geometry of Curves and Surfaces, Dover Publications, Inc., New York 1960
4 J. Park, Lorentzian submanifolds in Lorentzian space form with the same constant curvatures, Geom. Dedicata 108 (2004), 93-104   DOI
5 J. Park, Lorentzian surfaces with constant curvatures and transformations in the 3-dimensional Lorentzian space, J. Korean Math. Soc. 45 (2008), no. 1, 41-61   과학기술학회마을   DOI   ScienceOn
6 K. Tenenblat, Backlund's theorem for submanifolds of space forms and a generalized wave equation, Bol. Soc. Brasil. Mat. 16 (1985), no. 2, 69-94   DOI
7 K. Tenenblat and C. L. Terng, Backlund's theorem for n-dimensional submanifolds of $R^{2n-1}$, Ann. of Math. (2) 111 (1980), no. 3, 477-490   DOI
8 C. L. Terng, A higher dimension generalization of the sine-Gordon equation and its soliton theory, Ann. of Math. (2) 111 (1980), no. 3, 491-510   DOI
9 C. L. Terng, Soliton equations and differential geometry, J. Differential Geom. 45 (1997), no. 2, 407-445   DOI
10 K. Uhlenbeck, Harmonic maps into Lie groups: classical solutions of the chiral model, J. Differential Geom. 30 (1989), no. 1, 1-50   DOI