Ribaucour transformations for isometric immersions of pseudo-Riemannian space forms

DOI10.1016/J.GEOMPHYS.2009.03.002zbMath1171.53008OpenAlexW1993768992WikidataQ115353362 ScholiaQ115353362MaRDI QIDQ1021782

Qiaoling Xia

Publication date: 9 June 2009

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2009.03.002

zbMATH Keywords

Ribaucour transformationloop group actionpseudo-Riemannian space form

Mathematics Subject Classification ID

Soliton equations (35Q51) Surfaces in Euclidean and related spaces (53A05) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Cites Work

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• Isometric immersions of pseudo-Riemannian space forms
• Harmonic maps into Lie groups (classical solutions of the chiral model)
• Submanifolds of constant sectional curvature in pseudo-Riemannian manifolds
• Soliton equations and differential geometry
• Isometric immersions of space forms and soliton theory
• Isometric immersions of space forms in space forms
• The submanifold geometries associated to Grassmannian systems
• Darboux transformations for the twisted so(p, q) system and local isometric immersion of space forms
• Bäcklund transformations and loop group actions
• Isometric immersions of space forms into Riemannian and pseudo-Riemannian spaces of constant curvature
• Bäcklund's theorem for submanifolds of space forms and a generalized wave equation

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