Marginally trapped submanifolds in Lorentzian space forms and in the Lorentzian product of a space form by the real line

Abstract

We give local, explicit representation formulas for n-dimensional spacelike submanifolds which are marginally trapped in the Minkowski space R1n+2, the de Sitter space d𝕊n+2, the anti-de Sitter space Ad𝕊n+2 and the Lorentzian products 𝕊n+1 × ℝ and ℍn+1 × ℝ of the sphere and the hyperbolic space by the real line.