I'm a curious student about the Yamabe-type problem in Lorentzian geometry. I found a single article about this topic (2015).
I don't know much about Lorentzian geometry and I wonder if one may refers to this subject in a different way. For example, are Minkowsky spaces or hyperbolic manifolds equivalent to Lorentzian manifolds? I mean, articles that solve hyperbolic Yamabe problem or treat Minkowsky conformal invariants are related to the Yamabe problem in Lorentzian manifolds?
Could you give me a brief explanation about those spaces and the difference between them? Also, if someone is aware of recent progress in this area, it would be interesting.
Thank you in advance.