We present the transverse flux correlation function of the Lyman- \alpha forest in quasar absorption spectra at z \sim 2.1 from VLT-FORS and VLT-UVES observations of a total of 32 pairs of quasars ; 26 pairs with separations in the range 0.6 < \theta < 4 arcmin and 6 pairs with 4 < \theta < 10 arcmin .
Correlation is detected at the 3 \sigma level up to separations of the order of \sim 4 arcmin ( or \sim 4.4 h ^ { -1 } Mpc comoving at z = 2.1 for \Omega _ { m } = 0.3 and \Omega _ { \Lambda } = 0.7 ) .
We have , furthermore , measured the longitudinal correlation function at a somewhat higher mean redshift ( z = 2.39 ) from 20 lines of sight observed with high spectral resolution and high signal-to-noise ratio with VLT-UVES .
We compare the observed transverse and longitudinal correlation functions to that obtained from numerical simulations and illustrate the effect of spectral resolution , thermal broadening and peculiar motions .
The shape and correlation length of the correlation functions are in good agreement with those expected from absorption by the filamentary and sheet-like structures in the photoionized warm intergalactic medium predicted in CDM-like models for structures formation .
Using a sample of 139 C iv systems detected along the lines of sight toward the pairs of quasars we also investigate the transverse correlation of metals on the same scales .
The observed transverse correlation function of intervening C iv absorption systems is consistent with that of a randomly distributed population of absorbers .
This is likely due to the small number of pairs with separation less than 2 arcmin .
We detect , however , a significant overdensity of systems in the sightlines towards the quartet Q 0103 - 294A & B , Q 0102 - 2931 and Q 0102 - 293 which extends over the redshift range 1.5 \leq z \leq 2.2 and an angular scale larger than 10 arcmin .