Conformal Killing vector fields and a virial theorem
  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. 
Jos\'e F. Cari\~nena, Irina Gheorghiu, Eduardo Mart\'inez and   Patr\'icia Santos
math-ph gr-qc math.MP