We then consider the cosmological evolution of the aether, arguing that the vector will naturally evolve to be orthogonal to constant-density hypersurfaces in a Friedmann-Robertson-Walker cosmology. ❋ Sean (2008)
Your candidate should be able to quasi-exponentially 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. ❋ Mark (2007)
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. ❋ 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. ❋ Sun Bin (2006)
One way to do this is by means of additional Lorentz invariant dynamical structure, for example a suitable time-like 4-vector field, that permits the definition of a foliation of space-time into space-like hypersurfaces providing a Lorentz invariant notion of "evolving configuration" and along which nonlocal effects are transmitted. ❋ Goldstein, Sheldon (2006)
In Figure 1 the planes represent the hypersurfaces of simultaneity. ❋ 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. ❋ Faye, Jan (2005)
Σ² M² are spacelike hypersurfaces in hole-free spacetimes ❋ Earman, John (2004)
M² be spacelike hypersurfaces of their respective spacetimes. ❋ 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. ❋ DiSalle, Robert (2002)
Hyperspace contains not only an infinite number of flat 3-spaces like ours but also an infinite number of curved 3-spaces or hypersurfaces of different types. ❋ Unknown (1910)
Just as portions of our space are bounded by surfaces, plane or curved, so portions of hyperspace are bounded by hypersurfaces (three-dimensional), i. e., flat or curved 3-spaces. ❋ Unknown (1910)
In the same way that we have curved surfaces in ordinary space to which we can apply the non-Euclidean geometries of two dimensions, so in space of four dimensions we have curved spaces or hypersurfaces to which we can apply the non-Euclidean geometries of three dimensions, and some have taken this fact as completing the explanation of these geometries, eroneously supposing that they assume our space to be a curved space in space of four dimensions. ❋ Unknown (1910)
