  We present the results of molecular line observations performed toward the
NGC 2068 and NGC 2071 regions of the Orion B cloud as the TRAO-FUNS project to
study the roles of the filamentary structure in the formation of dense cores
and stars in the clouds. Gaussian decomposition for the C$^{18}$O spectra with
multiple velocity components and application of a Friends-of-Friends algorithm
for the decomposed components allowed us to identify a few tens of velocity
coherent filaments. We also identified 48 dense cores from the observations of
N$_2$H$^{+}$ using a core finding tool, FellWalker. We made the virial analysis
for these filaments and dense cores, finding that the filaments with
N$_2$H$^{+}$ dense core are thermally supercritical, and the filaments with
larger ratio between the line mass and the thermal critical line mass tend to
have more dense cores. We investigated the contribution of the nonthermal
motions in dense cores and filaments, showing the dense cores are mostly in
transonic/subsonic motions while their natal filaments are mostly in supersonic
motions. This may indicates that gas turbulent motions in the filaments have
been dissipated at the core scale to form the dense cores there. The filaments
with (dynamically evolved) dense cores in infalling motions or with NH$_2$D
bright (or chemically evolved) dense cores are all found to be gravitationally
critical. Therefore, the criticality of the filament is thought to provide a
key condition for its fragmentation, the formation of dense cores, and their
kinematical and chemical evolution.
