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Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Codimension two spacelike submanifolds of the Lorentz-Minkowski spacetime into the light cone
Part of
- Global differential geometry
- Local differential geometry
Luis J. Alías, Verónica L. Cánovas, Marco Rigoli
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 149 / Issue 6 / December 2019

Published online by Cambridge University Press:

17 January 2019, pp. 1523-1553

Print publication:

December 2019
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Following an original idea of Palmas, Palomo and Romero, recently developed in [12], we study codimension two spacelike submanifolds contained in the light cone of the Lorentz-Minkowski spacetime through an approach which allows us to compute their extrinsic and intrinsic geometries in terms of a single function u. As the first application of our approach, we classify the totally umbilical ones. For codimension two compact spacelike submanifolds into the light cone, we show that they are conformally diffeomorphic to the round sphere and that they are given by an explicit embedding written in terms of u. In the last part of the paper, we consider the case where the submanifold is (marginally, weakly) trapped. In particular, we derive some non-existence results for weakly trapped submanifolds into the light cone.