Conformal Killing vectors and virial theorems
By Patrícia Santos (Polytechnic Institute of Coimbra)
A virial theorem is formulated for a Lagrangian mechanical system on a Riemannian manifold and is given in generalised coordinates (see e.g.  and references therein and also  for a more general approach in Lie algebroid formalism). The special case of an affine virial function is studied and a spherical geometry problem is analysed using this approach. The particular cases of an affine virial function associated to a Killing vector field on the base manifold, homothetic or conform Killing are considered and virial theorems are established for each case.
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 J.F. Cariñena, I. Gheorghiu, E. Martínez and P. Santos: Virial theorem in quasicoordinates and Lie algebroid formalism. Int. J. Geom. Methods Mod. Phys. 11, 1450055 (9pp) (2014).