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http://dx.doi.org/10.4134/CKMS.2006.21.4.729

RIBAUCOUR TRANSFORMATIONS ON RIEMANNIAN SPACE FORMS IN LORENTZIAN SPACE FORM  

Park, Joon-Sang (Department of Mathematics Dongguk University)
Publication Information
Communications of the Korean Mathematical Society / v.21, no.4, 2006 , pp. 729-737 More about this Journal
Abstract
We study Ribaucour transformations on nondegenerate local isometric immersions of Riemannian space forms into Lorentzian space forms with flat normal bundles. They can be explained by dressing actions on the solution space of Lorentzian Grassmannian systems.
Keywords
isometric immersion; space forms; flat connection; nondegenerate; Lorentzian Grassmannian system;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 C. L. Terng, Soliton equations and differential geometry, Jour. Diff. Geom. 45(1997), 407-445   DOI
2 K. Uhlenbeck, Harmonic maps into Lie group (classical solutions of the Chiral model), Jour. Diff. Geom. 30 (1989), 1-50   DOI
3 C. L. Terng, A higher dimensional generalization of the sine-Gordon equation and its soliton theory, Ann. Math. 111 (1980), 491-510   DOI
4 M. Bruck, X. Du, J. Park, and C. L. Terng, The submanifold geometry of real Grassmannian systems, Mem. Amer. Math. Soc. 155 (2002), No. 735
5 E. Cartan, Sur les uarietes de courbure constante d 'un espace euclidien ou noneuclidien, Bull. Soc. Math. France 47 (1920), 125-160
6 D. Hilbert, Uber Flachen von konstanter Gausscher Krummung, Trans. Amer. Math. Soc. 2 (1901), 89-99
7 B. O'Neill, Semi-Riemannian Geometry, Academic Press, 1983
8 R. Palais and C. L. Terng, Critical Point Theory and Submanifold Geometry, Springer- Verag, LNM 1353, 1988
9 J. Park,, Riemannian submanifolds in Lorentzian manifolds with the same constant curvatures, Bull. Korean Math. Soc. 39 (2002), 237-249   DOI
10 K. Tenenblat, Backlund's theorem for submanifolds of space forms and a generalized wave equation, Boll. Soc. Brasil. Mat. 16 (1985), 67-92
11 K. Tenenblat and C. L. Terng, Backlund's theorem for n-dimensional submanifolds of $R^{2n-1}$, Ann. Math. 111 (1980), 477-490   DOI