Definitions
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 noun Plural form of
hypersurface .
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Examples

We then consider the cosmological evolution of the aether, arguing that the vector will naturally evolve to be orthogonal to constantdensity hypersurfaces in a FriedmannRobertsonWalker cosmology.
Ripples in the Aether Sean 2008

Your candidate should be able to quasiexponentially expand the universe, flatten out its spatial hypersurfaces, causally connect seemingly unconnected regions of the microwave sky, generate all the matter content of later epochs (reheating) and imprint upon it the density perturbations necessary to seed our observed large scale structure.

We imagined that there were some hypothetical vector field that had a nonzero value in empty space, but which (basically) pointed along a timelike direction, orthogonal to hypersurfaces of constant cosmological time.
Anatomy of a Paper: Part II, Calculation Sean 2007

Huisken was working on the Mean Curvature Flow for hypersurfaces,which closely parallels the Ricci Flow,being the most natural flows for intrinsic and extrinsic curvature respectively.
Quick note: Yau vs New Yorker Sun Bin 2006

One way to do this is by means of additional Lorentz invariant dynamical structure, for example a suitable timelike 4vector field, that permits the definition of a foliation of spacetime into spacelike hypersurfaces providing a Lorentz invariant notion of "evolving configuration" and along which nonlocal effects are transmitted.
Bohmian Mechanics Goldstein, Sheldon 2006

In Figure 1 the planes represent the hypersurfaces of simultaneity.
Backward Causation Faye, Jan 2005

But neither with respect to the frame S* nor S** is the tachyon source at rest and the hypersurfaces are therefore tilted in relation to the arrow of trajectory.
Backward Causation Faye, Jan 2005

Î£² M² are spacelike hypersurfaces in holefree spacetimes
Time Machines Earman, John 2004

M² be spacelike hypersurfaces of their respective spacetimes.
Time Machines Earman, John 2004

The spacetime structure that is implied by special relativity is thus an affine space, like Newtonian spacetime, but it is not objectively divided into hypersurfaces of absolute simultaneity; the sets of simultaneous events for any inertial frame are the hyperplanes orthogonal to the trajectories that determine that frame.
Space and Time: Inertial Frames DiSalle, Robert 2002
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