On time-like surfaces of positive constant Gaussian curvature and imaginary principal curvatures

DOI10.1016/S0393-0440(01)00066-3zbMath1084.37059OpenAlexW1982347132MaRDI QIDQ1602445

Jun-Ichi Inoguchi, Chao-Hao Gu, He-Sheng Hu

Publication date: 23 June 2002

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

Full work available at URL: https://doi.org/10.1016/s0393-0440(01)00066-3

zbMATH Keywords

Bäcklund transformationsDarboux transformationscosh-Gordon equationTime-like surfaces

Mathematics Subject Classification ID

Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Non-Euclidean differential geometry (53A35) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (9)

Generalized Weierstrass representations of surfaces with the constant Gauss curvature in pseudo-Riemannian three-dimensional space forms ⋮ Bäcklund transformation for non-lightlike curves in Minkowski 3-space ⋮ Lorentz-conformal transformations in the plane ⋮ Unnamed Item ⋮ Superposition formulae for the geometric Bäcklund transformations of the hyperbolic and elliptic sine-Gordon and sinh-Gordon equations ⋮ Isometric immersions of pseudo-Riemannian space forms ⋮ Time-like surfaces in the Lorentz-Minkowski space with prescribed Gaussian curvature and Gauss map ⋮ Time-like linear Weingarten surfaces in Lorentzian space forms ⋮ Bäcklund theorems in three-dimensional de Sitter space and anti-de Sitter space

Cites Work

• Bäcklund transformations and their applications
• Timelike surfaces of constant mean curvature in Minkowski 3-space
• Darboux transformations between \(\Delta \alpha=\text{sinh}\alpha\) and \(\Delta\alpha=\sin \alpha\) and the application to pseudo-spherical congruences in \(\mathbb{R}^{2,1}\)
• Bäcklund transformation on surfaces with \(K=-1\) in \(\mathbb{R}^{2,1}\)
• Darboux transformations on timelike constant mean curvature surfaces
• Bäcklund transformations for surfaces in Minkowski space
• Harmonic Maps and Classical Surface Theory in Minkowski 3-Space
• On the harmonic maps from R 1,1 to S 1,1.
• The construction of hyperbolic surfaces in 3 dimensional minkowski space and sinh-laplace equation
• The solitons in some geometrical field theories
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