Classification of Lorentzian surfaces with parallel mean curvature vector in pseudo-Euclidean spaces

DOI10.1016/j.jmaa.2010.04.022zbMath1196.53015OpenAlexW1989636069WikidataQ125101601 ScholiaQ125101601MaRDI QIDQ986568

Yu Fu, Zhong Hua Hou

Publication date: 11 August 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.04.022

zbMATH Keywords

parallel mean curvature vectorpseudo-Euclidean spacemarginally trapped surfaceLorentzian surface

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Local submanifolds (53B25) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (5)

Quasi-minimal Lorentz surfaces with pointwise 1-type Gauss map in pseudo-Euclidean 4-space ⋮ SOME CLASSIFICATIONS OF LORENTZIAN SURFACES WITH FINITE TYPE GAUSS MAP IN THE MINKOWSKI 4-SPACE ⋮ Surfaces with parallel normalized mean curvature vector field in Euclidean or Minkowski 4-space ⋮ Biharmonic submanifolds with parallel mean curvature vector in pseudo-Euclidean spaces ⋮ On the biconservative quasi-minimal immersions into semi-Euclidean spaces

Cites Work

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• Isometric immersions of Lorentz space with parallel second fundamental forms
• Complete classification of parallel surfaces in 4-dimensional Lorentzian space forms
• Nonlinear Klein-Gordon equations and Lorentzian minimal surfaces in Lorentzian complex space forms
• Classification of quasi-minimal surfaces with parallel mean curvature vector in pseudo-Euclidean 4-space \({\mathbb E}^4_2\)
• Addendum to ``classification of marginally trapped Lorentzian flat surfaces in \(\mathbb E_2^4\) and its application to biharmonic surfaces
• Complete classification of spatial surfaces with parallel mean curvature vector in arbitrary non-flat pseudo-Riemannian space forms
• Classification of marginally trapped Lorentzian flat surfaces in \(\mathbb E^4_2\) and its application to biharmonic surfaces
• Marginally trapped surfaces in Lorentzian space forms with positive relative nullity
• Classification of spatial surfaces with parallel mean curvature vector in pseudo-Euclidean spaces of arbitrary dimension
• Dependence of the Gauss-Codazzi equations and the Ricci equation of Lorentz surfaces
• Submanifolds with Constant Mean Curvature
• Gravitational Collapse and Space-Time Singularities
• The Large Scale Structure of Space-Time

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