Can somebody help me with this relativity question?

Question

ivancsc1996 · Answer

What I mean is, when Dirac defines a tensor, he uses the general definition used in tensor calculus$$x ^{\mu'}=x^{\mu'}_{,\mu}x ^{\mu}$$Non the less I has understood Lorentz tensors were defined as$$x^{\mu'}=\Lambda^{\mu'}_{\mu}x^{\mu}$$where lambda is the tensor for Lorentz transformations. So, 

1) Are Lorentz transformations in flat spacetime the same as those in curved space time?

2) Are both definition of a tensor in spacetime equivalent?

Thank you!

anonymous · Answer

Lorentz transformations are not the same in flat (Euclidean) vs. Curved (relativistic) geometries of space. I don't think.

ivancsc1996 · Answer

But flat doesn't necessarily mean Euclidian. You can hav a flat minkawski (relativistic) spacetime. You just need that whatever your metric tensor is, it satisfies that the curvature tensor is 0.