The Signature problem for embedded space-times

The compatibility between general relativity and the property that spacetimes are ebeddable manifolds is further examined. It is shown that the signature of the embedding space is uniquely determined provided the embedding space is real and its dimension is kept to the minimal. Signature changes produce complex embeddings which in turn may induce topological changes in the space-time. Space-time signature preserving symmetries identify the twisting vector as a real connection on space-time whose curvature is described by the Ricci’s equation in terms of the second fundamental form.