in coordinates the infinitesimal isometries of minkowski space are 3 boosts and 3 rotations (and 4 displacements).

I.e

where are killing vectors given by , , , , and

I am probably being really thick, but what are the killing vectors that preserve the surfaces of I am totally confused, or atleast how do I work them out? I expect there should be three such vectors, and are linear combinations of the above vectors.

If these where constant t surfaces, then this would be easy, it's just 3 rotations, but i need to know , where the constant could be zero I suppose if that makes it easier.