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

TL;DR

This paper provides explicit local formulas for describing marginally trapped spacelike submanifolds in various Lorentzian space forms, including Minkowski, de Sitter, anti de Sitter, and product spaces.

Contribution

It introduces new explicit representation formulas for marginally trapped submanifolds in several Lorentzian space forms, expanding understanding of their geometric structure.

Findings

Explicit formulas for submanifolds in Minkowski, de Sitter, anti de Sitter spaces

Representation in Lorentzian products of sphere and hyperbolic space

Enhanced geometric understanding of marginally trapped submanifolds

Abstract

We give local, explicit representation formulas for n-dimensional spacelike submanifolds which are marginally trapped in the Minkowski space, the de Sitter and anti de Sitter spaces and the Lorentzian products of the sphere and the hyperbolic space by the real line.