Originally Posted by

**Ans**
With easy. It is enough to just copy-paste first reference from article: S. Hawking, J. Ellis, The Large Scale Structure of Spacetime, published by Mir, 1977

If you would find English version, look at chapter 5 (if I remember number correctly). In that part, there is prove that it is impossible to have inscribed hypersurface with signature of metric different from signature of space metric.

Signature of metric for 4d Euclidean space is (1,1,1,1). Signature of metric for Minkowski space, for Lorentz transformation, is (1,1,1,-1). Signature of metric for Lorentz-like transformation is (surprise-surprise) (1,1,1,-1)

So, it is impossible to build hypersurface in Euclidean space with metric (1,1,1,-1) , and it affect both Lorentz-like transformation and Lorentz transformation. Lorentz transformation is just one of Lorentz-like transformations