  We analyze two types of relativistic simultaneity associated to an observer:
the spacelike simultaneity, given by Landau submanifolds, and the lightlike
simultaneity (also known as observed simultaneity), given by past-pointing
horismos submanifolds. We study some geometrical conditions to ensure that
Landau submanifolds are spacelike and we prove that horismos submanifolds are
always lightlike. Finally, we establish some conditions to guarantee the
existence of foliations in the space-time whose leaves are these submanifolds
of simultaneity generated by an observer.
