대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제21권1호
  • /
  • Pages.165-175
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  • 2006
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  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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RIBAUCOUR TRANSFORMATIONS OF THE SURFACES WITH CONSTANT POSITIVE GAUSSIAN CURVATURES IN THE 3-DIMENSIONAL EUCLIDEAN SPACE

  • 발행 : 2006.01.01
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초록

We associate the surfaces of constant Gaussian curvature K = 1 with no umbilics to a subclass of the solutions of $O(4,\;1)/O(3){\times}O(1,\;1)-system$. From this correspondence, we can construct new K = 1 surfaces from a known K = 1 surface by using a kind of dressing actions on the solutions of this system.

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참고문헌

  1. L. Bianchi, Vorlesungen uber Differentialgeometrie, Leipzig, Berlin, Druck und Verlag von B. G. Teubner (1910)
  2. 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
  3. F. Burtall, Isothermic surfaces: conformal geometry, Cifford algebras and integrable systems, Intergrable systems, Geometry and Topology, International Press, to appear
  4. J. Inoguch, Characterizations of Backlund transformations of constant mean curvature surfaces, International Jour Math. 16 (2005), 101-110 https://doi.org/10.1142/S0129167X05002801
  5. U. Hertrich-Jeromin and F. Pedit, Remarks on the Darboux transform of isothermic surfaces, Doc. Math. 2 (1997), 313-333
  6. J. Park, Riemannian submanifolds in Lorentzian mamifolds with the some constant curvatures, Bull. Korean Math. Soc. 39 (2002), 93-104
  7. J. Park, Lorentzian submanifolds in Lorentzian space form with the same constant curvatures, Geom. Ded. 108 (2004), 93-104 https://doi.org/10.1007/s10711-004-5458-0
  8. C. L. Terng, Soliton equations and differential geometry, Jour. Diff. Geom. 45 (1997), 407-445 https://doi.org/10.4310/jdg/1214459804