  (abridged) We used the wide-field IFU spectrograph PMAS/PPAK at the 3.5m
telescope of Calar Alto Observatory to observe six nearby spiral galaxies that
hosted SNe Ia. Spatially resolved 2D maps of the properties of the ionized gas
and the stellar populations were derived. Five of the observed galaxies have an
ongoing star formation rate of 1-5 M_sun/yr and mean stellar population ages ~5
Gyr. The sixth galaxy shows no star formation and has an about 12 Gyr old
stellar population. All galaxies have stellar masses larger than 2E+10 M_sun
and metallicities above solar. Four galaxies show negative radial metallicity
gradients of the ionized gas up to -0.058 dex/kpc and one has nearly uniform
metallicity with a possible shallow positive slope. The stellar components show
shallower negative metallicity gradients up to -0.03 dex/kpc. We find no clear
correlation between the properties of the galaxy and those of the supernovae,
which may be because of the small ranges spanned by the galaxy parameters.
However, we note that the Hubble residuals are on average positive while
negative Hubble residuals are expected for SNe Ia in massive hosts such as the
galaxies in our sample. In conclusion, IFU spectroscopy on 4-m telescopes is a
viable technique for studying host galaxies of nearby SNe Ia. It allows one to
correlate the supernova properties with the properties of their host galaxies
at the projected positions of the supernovae. Our current sample of six
galaxies is too small to draw conclusions about the SN Ia progenitors or
correlations with the galaxy properties, but the ongoing CALIFA IFU survey will
provide a solid basis to exploit this technique more and improve our
understanding of SNe Ia as cosmological standard candles.
