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Lorentzian surfaces with constant curvatures and transformations in the 3-dimensional Lorentzian space

박준상
대한수학회 (The Korean Mathematical Society)|2008.01|대한수학회지 (Journal of the KMS)|제45권 제1호|pp. 41-61

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참고문헌

키워드

spacelike surfacemean curvatureGaussian curvaturetimelike surface(elliptic) sine-Gordon(hyperbolic) sinh-GordonGrassmannian system
주제분류수학

초록

We study Lorentzian surfaces with the constant Gaussian curvatures or the constant mean curvatures in the 3-dimensional Lorentzian space and their transformations. Such surfaces are associated to the Lorentzian Grassmannian systems and some transformations on such surfaces are given by dressing actions on those systems.

Abstract

We study Lorentzian surfaces with the constant Gaussian curvatures or the constant mean curvatures in the 3-dimensional Lorentzian space and their transformations. Such surfaces are associated to the Lorentzian Grassmannian systems and some transformations on such surfaces are given by dressing actions on those systems.

참고문헌 (11)

  1. M. Bruck, "The submanifold geometries associated to Grassmannian systems", Memoirs of the American Mathematical Society, 155(735) (2002)
  2. S. S. Chern, "Geometrical interpretations of the sinh-Gordon equation", Annales Polonici Mathematici, 39, pp.74~80 (1980)
  3. M. Dajczer, "Commuting Codazzi tensors and the Ribaucour transformation for submanifolds", Results in Mathematics, 44(3), pp.258~278 (2003)
  4. L. P. Eisenhart, "A Treatise on the Differential Geometry of curves and Surfaces" (1960), Dover
  5. J. Inoguch, "Timelike Surfaces of constant mean curvature in Minkowski 3-space", TOKYO JOURNAL MATHEMATICS, 21(1), pp.141~152 (1998)
  6. J. Inoguch, "Darboux transformations on timelike constant mean curvature surfaces", Journal of Geometry and Physics, 32(1), pp.57~78 (1999)
  7. B. O’Neill, "Semi-Riemannian Geometry" (1983), Academic Press
  8. B. Palmer, "Backlund transformation for surfaces in Minkowski space", Journal of Mathematical Physics, 31(12), pp.2872~2875 (1990)
  9. C. L. Terng, "Soliton equations and differential geometry", Journal of Differential Geometry, 45(2), pp.407~445 (1997)
  10. C. Tian, "Backlund transformations on surfaces with K = -1 in R2,1", Journal of Geometry and Physics, 22(3), pp.212~218 (1997)
  11. T. Weinstein, "An Introduction to Lorentz surfaces", De Gruyter Expositions in Mathematics, 22 (1996), Walter de Gruyter

관련 논문AI추천

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