  We investigate the relation between galaxy structure and star formation rate
(SFR) in a sample of $\sim2.9\times10^{4}$ central galaxies with $z<0.0674$ and
axial ratios $b/a>0.5$. The star-forming main sequence (SFMS) shows a bend
around the stellar mass of $M_\ast\leq{}M_c=2\times10^{10}{}M_{\odot}$. At
$M_\ast\leq{}M_c$ the SFMS follows a power-law
$\text{SFR}\propto{}M_\ast^{0.85}$, while at higher masses it flattens. $M_c$
corresponds to a dark matter halo mass of
$M_\text{vir}\sim{}10^{11.8}M_{\odot}$ where virial shocks occurs. Some galaxy
structure (e.g., half-light radius, $R_e$) exhibits a non-monotonic dependence
across the SFMS at a fixed $M_\ast$. We find $\text{SFR}\propto{R_e^{-0.28}}$
at fixed $M_\ast$, consistent with the global Kennicutt-Schmidt (KS) law. This
finding suggests that galaxy sizes contribute to the scatter of the SFMS.
However, at $M_\ast>M_c$ the relationship between SFR and $R_e$ diminishes.
Low-mass galaxies above the mean of the SFMS have smaller radii, exhibit
compact and centrally concentrated profiles resembling green valley (GV) and
quiescent galaxies at the same mass, and have higher
$M_{\text{H}_2}/M_\text{HI}$. Conversely, those below the SFMS exhibit larger
radii, lower densities, have no GV or quiescent counterparts at their mass and
have lower $M_{\text{H}_2}/M_\text{HI}$. The above data suggest two pathways
for quenching low-mass galaxies, $M_\ast\leq{}M_c$: a fast one that changes the
morphology on the SFMS and a slow one that does not. Above $M_c$, galaxies
below the SFMS resemble GV and quiescent galaxies structurally, implying that
they undergo a structural transformation already within the SFMS. For these
massive galaxies, CG are strongly bimodal, with SFMS galaxies exhibiting
negative color gradients, suggesting most star formation occurs in their
outskirts, maintaining them within the SFMS.
