  We have studied the filaments extracted from the column density maps of the
nearby Lupus 1, 3, and 4 molecular clouds, derived from photometric maps
observed with the Herschel satellite. Filaments in the Lupus clouds have quite
low column densities, with a median value of $\sim$1.5$\times$10$^{21}$
cm$^{-2}$ and most have masses per unit length lower than the maximum critical
value for radial gravitational collapse. Indeed, no evidence of filament
contraction has been seen in the gas kinematics. We find that some filaments,
that on average are thermally subcritical, contain dense cores that may
eventually form stars. This is an indication that in the low column density
regime, the critical condition for the formation of stars may be reached only
locally and this condition is not a global property of the filament. Finally,
in Lupus we find multiple observational evidences of the key role that the
magnetic field plays in forming filaments, and determining their confinement
and dynamical evolution.
