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We study the link between the kinematic-morphology of galaxies, as inferredfrom integral-field stellar kinematics, and their relation between mass andstar formation rate (SFR). Our sample consists of $\sim 3200$ galaxies withintegral-field spectroscopic data from the MaNGA survey with availabledeterminations of their effective stellar angular momentum within thehalf-light radius $\lambda_{R_e}$. We find that for star-forming galaxies,namely along the star formation main sequence (SFMS), the $\lambda_{R_e}$values remain large and almost unchanged over about two orders of magnitude instellar mass, with the exception of the lowest masses$\mathcal{M}_{\star}\lesssim2\times10^{9} \mathcal{M}_{\odot}$, where$\lambda_{R_e}$ slightly decreases. The SFMS is dominated by spiral galaxieswith small bulges. Below the SFMS, but above the characteristic stellar mass$\mathcal{M}_{\rm crit}\approx2\times10^{11} \mathcal{M}_{\odot}$, there is asharp decrease in $\lambda_{R_e}$ with decreasing star formation rate: massivegalaxies well below the SFMS are mainly slow-rotator early-type galaxies,namely genuinely spheroidal galaxies without disks. Below the SFMS and below$\mathcal{M}_{\rm crit}$ the decrease of $\lambda_{R_e}$ with decreasing SFRbecomes modest or nearly absent: low-mass galaxies well below the SFMS, arefast-rotator early-type galaxies, and contain fast-rotating stellar disks liketheir star-forming counterparts. We also find a small but clear environmentaldependence for the massive galaxies: in the mass range $10^{10.9}-10^{11.5}\mathcal{M}_{\odot}$, galaxies in rich groups or denser regions or classifiedas central galaxies have lower values of $\lambda_{R_e}$. While noenvironmental dependence is found for galaxies of lower mass. We discuss howour results can be understood as due to the different star formation and massassembly histories of galaxies with varying mass.

SDSS-IV MaNGA: The kinematic-morphology of galaxies on the mass vs star-formation relation in different environments