  The virial theorem is formulated both intrinsically and in local coordinates
for a Lagrangian system of mechanical type on a Riemann manifold. An import
case studied in this paper is that of an affine virial function associated to a
vector field on the configuration manifold. The special cases of a virial
function associated to a Killing, a homothetic and a conformal Killing vector
field are considered and the corresponding virial theorems are established for
this type of functions.
