I'm trying to find the Killing vectors for de Sitter space using global coordinates, i.e. the spherical foliation. In the end, I want to know how to perform a boost on the 1+1 and 3+1 de Sitter manifolds so that I can make two points lie at the same spatial position (the spatial origin). I know how to perform a Lorentz transformation in Minkowski, but not for curved spacetimes.
Two things I've tried are re-deriving the Lorentz transformations for a curved space using the steps on the Wikipedia page for Lorentz transformations, as well as performing a regular Lorentz transformation on the hyperboloid embedded in a higher dimension.