Browse > Article
http://dx.doi.org/10.4134/JKMS.2008.45.1.041

LORENTZIAN SURFACES WITH CONSTANT CURVATURES AND TRANSFORMATIONS IN THE 3-DIMENSIONAL LORENTZIAN SPACE  

Park, Joon-Sang (Department of Mathematics Dongguk University)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.1, 2008 , pp. 41-61 More about this Journal
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.
Keywords
spacelike surface; timelike surface; Gaussian curvature; mean curvature; (elliptic) sine-Gordon; (hyperbolic) sinh-Gordon; Grassmannian system;
Citations & Related Records

Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
연도 인용수 순위
1 L. P. Eisenhart, A Treatise on the Differential Geometry of curves and Surfaces, Dover, 1960
2 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
3 S. S. Chern, Geometrical interpretations of the sinh-Gordon equation, Ann. Polon. Math. 39 (1980), 74-80
4 M. Dajczer and R. Tojeiro, Commuting Codazzi tensors and the Ribaucour transformation for submanifolds, Results Math. 44 (2003), no. 3-4, 258-278   DOI
5 J. Inoguch, Timelike Surfaces of constant mean curvature in Minkowski 3-pace, Tokyo J. Math. 21 (1998), no. 1, 141-152   DOI   ScienceOn
6 J. Inoguch, Darboux transformations on timelike constant mean curvature surfaces, J. Geom. Phys. 32 (1999), no. 1, 57-78   DOI   ScienceOn
7 B. O'Neill, Semi-Riemannian Geometry, Academic Press, 1983
8 B. Palmer, Backlund transformation for surfaces in Minkowski space, J. Math. Phys. 31 (1990), no. 12, 2872-2875   DOI
9 C. L. Terng, Soliton equations and differential geometry, J. Differential Geom. 45 (1997), no. 2, 407-445   DOI
10 C. Tian, Backlund transformations on surfaces with K = -1 in $R^{2,1}$, J. Geom. Phys. 22 (1997), no. 3, 212-218   DOI   ScienceOn
11 T. Weinstein, An Introduction to Lorentz surfaces, de Gruyter Expositions in Math., 22, Walter de Gruyter, Berlin, 1996