  We present an analysis of the distribution of 77 supernovae (SNe) Ia relative
to spiral arms of their Sab-Scd host galaxies, using our original measurements
of the SN distances from the nearby arms, and study their light curve decline
rates ($\Delta m_{15}$). For the galaxies with prominent spiral arms, we show
that the $\Delta m_{15}$ values of SNe Ia, which are located on the arms, are
typically smaller (slower declining) than those of interarm SNe Ia (faster
declining). We demonstrate that the SN Ia distances from the spiral arms and
their galactocentric radii are correlated: before and after the average
corotation radius, SNe Ia are located near the inner and outer edges (shock
fronts) of spiral arms, respectively. For the first time, we find a significant
correlation between the $\Delta m_{15}$ values and SN distances from the shock
fronts of the arms (progenitor birthplace), which is explained in the
frameworks of sub-Chandrasekhar-mass white dwarf explosion models and density
wave theory, where, respectively, the $\Delta m_{15}$ parameter and SN distance
from the shock front are appropriate progenitor population age (lifetime)
indicators.
