Definition of "hypersurface" [hypersurface]

• A n.-dimensional surface in a space (often a Euclidean space) of dimension n.+1 (noun)

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• "The Weyl curvature is zero on both the future boundary and past boundary, hence the Big Bang is still well-defined in the cyclic model as the unique hypersurface on which the Weyl curvature vanishes."
• "Now, in an open or flat Friedmann-Robertson-Walker cosmological model with no cosmological constant, whilst the past 'Big-Bang' singularity corresponds to a spacelike hypersurface in the boundary of the conformal compactification, the future timelike infinity corresponds to a single point."
• "The far future of our universe is therefore representable by de Sitter space-time, and in this type of space-time the future timelike boundary is a spacelike hypersurface."