논문KCI 등재
Ribaucour transformations on Lorentzian space forms in Lorentzian space forms
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초록
We study Ribaucour transformations on nondegenerate local isometric immersions of Lorentzian space forms into Lorentzian space forms with the same sectional curvatures which have flat normal bundles. They can be associated to dressing actions on the solution space of Lorentzian Grassmannian systems.
Abstract
We study Ribaucour transformations on nondegenerate local isometric immersions of Lorentzian space forms into Lorentzian space forms with the same sectional curvatures which have flat normal bundles. They can be associated to dressing actions on the solution space of Lorentzian Grassmannian systems.
참고문헌 (10)
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- L. P. Eisenhart, "A Treatise on The Differential Geometry of Curves and Surfaces", 1960Dover Publications, Inc.
- J. Park, "Lorentzian submanifolds in Lorentzian space form with the same constant curvatures", Geometriae Dedicata, 108, pp.93~104 (2004)
- 박준상, "Lorentzian surfaces with constant curvatures and transformations in the 3-dimensional Lorentzian space", 대한수학회지, 45(1), pp.41~61 (2008), 대한수학회
- K. Tenenblat, "B¨acklund’s theorem for submanifolds of space forms and a generalized wave equation", Boletim da Sociedade Brasileira de Matemática, 16(2), pp.69~94 (1985)
- K. Tenenblat, "B¨acklund’s theorem for n-dimensional submanifolds of R2n−1", Annals of Mathematics, 111(3), pp.477~490 (1980)
- C. L. Terng, "A higher dimension generalization of the sine-Gordon equation and its soliton theory", Annals of Mathematics, 111(3), pp.491~510 (1980)
- C. L. Terng, "Soliton equations and differential geometry", Journal of Differential Geometry, 45(2), pp.407~445 (1997)
- K. Uhlenbeck, "Harmonic maps into Lie groups: classical solutions of the chiral model", Journal of Differential Geometry, 30(1), pp.1~50 (1989)
관련 논문AI추천
Lorentzian surfaces with constant curvatures and transformations in the 3-dimensional Lorentzian space박준상대한수학회 · 대한수학회지2008 · 제45권 제1호Ribaucour transformations on Riemannian space forms in Lorentzian space form박준상대한수학회 · 대한수학회논문집2006 · 제21권 제4호Ribaucour transformation for flat $m$-submanifolds in $\Bbb{H}^{m+n}$Dafeng Zuo대한수학회 · 대한수학회논문집2006 · 제21권 제4호On the geometry of biconservative submanifolds in pseudo-Riemannian space formsLi Du, Tian Nie대한수학회 · 대한수학회보2025 · 제62권 제3호Ribaucour transformations of the Surfaces with constant positive Gaussian curvatures in the 3-dimensional Euclidean space박준상대한수학회 · 대한수학회논문집2006 · 제21권 제1호Maximal Hypersurfaces of (m+2)-Dimensional Lorentzian Space FormsUur Dursun경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2008 · 제48권 제1호
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