Abstract
Due to the growing interest in embeddings of spacetimes in higher dimensional spaces, we consider a special type of embedding. We prove that Robertson–Walker spacetimes can be embedded as centroaffine hypersurfaces and graph hypersurfaces in some affine spaces in such a way that the induced relative metrics are exactly the Lorentzian metrics on the Robertson–Walker spacetimes. Such realizations allow us to view Robertson–Walker spacetimes and their submanifolds as affine submanifolds in a natural way. Consequently, our realizations make it possible to apply the tools of affine differential geometry to study Robertson–Walker spacetimes and their submanifolds.
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