# 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. [1] and references therein and also [2] 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.

References

[1] J.F. Cariñena, F. Falceto and M.F. Rañada: A geometric approach to a generalized virial theorem. J. Phys. A: Math. Theor. 45, 395210 (19pp) (2012).

[2] 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).