  We analyze data from direct numerical simulations of homogeneous and
isotropic turbulence (at Re_\lambda \approx 280) and study the statistics of
curvature and torsion of Lagrangian trajectories in order to extract
informations on the geometry of small scale coherent structures in turbulent
flows. We find that, as previously observed by Braun et al and by Xu et al, the
high curvature statistics is dominated by large scale flow reversals where the
velocity magnitude assumes very low values. In order to focus on small-scales
signatures, we introduce a cutoff on the velocity amplitude and we study the
probability distribution of curvature conditioned only on those events when the
local velocity is not that small. In this way we are able to select
small-scales turbulent features, connected to vortex filaments. We show that
the conditioned curvature probability density is well reproduced by a
multifractal formalism, following previous calculations made for acceleration.
Finally, by studying the joint statistics of curvature and torsion we find
further evidences that intense events are dominated by helical type
trajectories.
