대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제21권4호
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  • Pages.739-747
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  • 2006
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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RIBAUCOUR TRANSFORMATION FOR FLAT m-SUBMANIFOLDS IN ℍm+n

  • Zuo, Dafeng (School of Mathematics Korea Institute for Advanced Study, Department of Mathematics University of Science and Technology)
  • 발행 : 2006.10.31
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초록

By using O(m+n, 1)/$O(m){\times}O(n,1)-system$, we give an analytic version of Ribaucour transformation for flat m-dimensional submanifolds in $\mathbb{H}^{m+n}$ with flat, non-degenerate normal bundle and free of weak umbilics, where $n{\geq}m-1$.

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참고문헌

  1. M. Bruck, X. Du, J. S. Park, and C.-L. Terng, The submanifold geometries associated to Grassmannian system, Mem. Amer. Math. Soc. 155 (2002), 735
  2. E. Cartan, Sur les varietes de courbure constante d'un espace Euclidean ou non-Euclidean, Bull. Soc. Math., France 47 (1919),125-160 and 48 (1920), 132-208
  3. M. Dajczer and R. Tojeiro, Isometric immersions and the generalized Laplace and elliptic sinh-Gordon equations, J. reine. angew. Math. 467 (1995), 109-147
  4. M. Dajczer and R. Tojeiro, An extension of the classical Ribaucour transformation, Proc. London Math. Soc. 85 (2002), 211-232
  5. D. Hilbert, Uber Flachen, Von Konstanter, Gausscher Krummung, Trans. Amer. Math. Soc. 2 (1901), 87-99 https://doi.org/10.2307/1986308
  6. J. D. Moore, Isometric immersions of space forms in space forms, Pacific J. Math. 40 (1972), 157-166 https://doi.org/10.2140/pjm.1972.40.157
  7. J. D. Moore, Submanifold of constant positive curvature I, Duke Math. J. 44 (1977), 449-484 https://doi.org/10.1215/S0012-7094-77-04421-0
  8. J. S. Park, Riemannian submanifolds in Lorentzian manifolds with the same constant curvatures, Bull. Korean Math. Soc. 39 (2002), no. 2, 237-249 https://doi.org/10.4134/JKMS.2002.39.2.237
  9. J. S. Park, Isometric immersions of manifolds into space forms with the same con-stant curvatures, Commun. Korean Math. Soc. 17 (2002), no. 1, 57-69 https://doi.org/10.4134/CKMS.2002.17.1.057
  10. J. S. Park, Lorentzian submanifolds in Lorentzian space form with the same con-stant curvatures, Geom. Dedicata 108 (2004), 93-104 https://doi.org/10.1007/s10711-004-5458-0
  11. F. Pedit, A non-immersion theorem for space forms, Comment. Math. Hekvetici 63 (1988), 672-674 https://doi.org/10.1007/BF02566784
  12. C.-L. Terng, Soliton equations and differential geometry, J. Diff. Geom. 45 (1997), 407-455 https://doi.org/10.4310/jdg/1214459804
  13. K. Tenenblat and C.-L. Terng, Backlund's theorem for n-dimensional submanifolds in R^{2n-1}$, Ann. of Math. 111 (1980), 477-490 https://doi.org/10.2307/1971105
  14. K. Tenenblat, Backlund theorems for submanifolds of space forms and a generalized wave equation, Boll. Soc. Brasil. Mat. 16 (1985), 67-92
  15. D. Zuo, Q. Chen and Y. Cheng, $G^{p,q}_{m,n}$-system II and diagonalizable time-like immersions in $R^{p,m}$, Inverse Problems 20 (2004), 319-329 https://doi.org/10.1088/0266-5611/20/2/001