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We present the results of molecular line observations performed toward theNGC 2068 and NGC 2071 regions of the Orion B cloud as the TRAO-FUNS project tostudy the roles of the filamentary structure in the formation of dense coresand stars in the clouds. Gaussian decomposition for the C$^{18}$O spectra withmultiple velocity components and application of a Friends-of-Friends algorithmfor the decomposed components allowed us to identify a few tens of velocitycoherent filaments. We also identified 48 dense cores from the observations ofN$_2$H$^{+}$ using a core finding tool, FellWalker. We made the virial analysisfor these filaments and dense cores, finding that the filaments withN$_2$H$^{+}$ dense core are thermally supercritical, and the filaments withlarger ratio between the line mass and the thermal critical line mass tend tohave more dense cores. We investigated the contribution of the nonthermalmotions in dense cores and filaments, showing the dense cores are mostly intransonic/subsonic motions while their natal filaments are mostly in supersonicmotions. This may indicates that gas turbulent motions in the filaments havebeen dissipated at the core scale to form the dense cores there. The filamentswith (dynamically evolved) dense cores in infalling motions or with NH$_2$Dbright (or chemically evolved) dense cores are all found to be gravitationallycritical. Therefore, the criticality of the filament is thought to provide akey condition for its fragmentation, the formation of dense cores, and theirkinematical and chemical evolution.

TRAO Survey of Nearby Filamentary Molecular clouds, the Universal  Nursery of Stars (TRAO-FUNS). III. Filaments and dense cores in the NGC 2068  and NGC 2071 regions of Orion B