Reduction of the codimension for lightlike isotropic submanifolds (Q1602451)

The paper deals with embeddings of \(n\)-dimensional semi-Riemannian manifolds into \(N\)-dimensional manifolds (the latter are mainly of constant curvature). The question is posed under which circumstances, an embedding is possible already in an \(N-1\)-dimensional manifold. One of the main ingredients for the result is: The answer is ``Yes'', if the transversal connection on the embedding is metric, and one further condition for the connection is fulfilled. The result is not fully analogous to the positive definite case, because for light-like (hyper-)surfaces, non-vanishing normal and tangential vectors may coincide. The appendix presents an example with an embedding into a 5-dimensional space of signature \((-,-,+,+,+)\).