Definition : relativistic (or not) hyperplane

A hyperplane of simultaneity is a geometric concept used mainly in relativistic physics.
In a four-dimensional orthonormal framework (three dimensions of space and one dimension of time), it represents the set of points in space-time that are considered simultaneous for a given observer; the hypersurface that contains all the events that, for him, occur at the same time.
This "hyperplane of the present", which is represented as a horizontal sheet, therefore actually represents a three-dimensional space.
R.H.