  A very simple criterion to ascertain if (D-2)-surfaces are trapped in
arbitrary D-dimensional Lorentzian manifolds is given. The result is purely
geometric, independent of the particular gravitational theory, of any field
equations or of any other conditions. Many physical applications arise, a few
shown here: a definition of general horizon, which reduces to the standard one
in black holes/rings and other known cases; the classification of solutions
with a (D-2)-dimensional abelian group of motions and the invariance of the
trapping under simple dimensional reductions of the
Kaluza-Klein/string/M-theory type. Finally, a stronger result involving closed
trapped surfaces is presented. It provides in particular a simple sufficient
condition for their absence.
