Using a sample of galaxies from the Sloan Digital Sky Survey (SDSS) Data
Release 4, we study the trends relating surface brightness profile type and
apparent axis ratio to the local galaxy environment. We use the SDSS parameter
`fracDeV' to quantify the profile type. We find that galaxies with M_r > -18
are mostly described by exponential profiles in all environments. Galaxies with
-21 < M_r < -18 mainly have exponential profiles in low density environments
and de Vaucouleurs profiles in high density environments. The most luminous
galaxies, with M_r < -21, are mostly described by de Vaucouleurs profiles in
all environments. For galaxies with M_r < -19, the fraction of de Vaucouleurs
galaxies is a monotonically increasing function of local density, while the
fraction of exponential galaxies is monotonically decreasing. For a fixed
surface brightness profile type, apparent axis ratio is frequently correlated
with environment. As the local density of galaxies increases, we find that for
-20 < M_r < -18, galaxies of all profile types become slightly rounder, on
average; for -22 < M_r < -20, galaxies with exponential profiles tend to become
flatter, while galaxies with de Vaucouleurs profiles become rounder; for M_r <
-22, galaxies with exponential profiles become flatter, while the de
Vaucouleurs galaxies become rounder in their inner regions, yet exhibit no
change in their outer regions. We comment on how the observed trends relate to
the merger history of galaxies.Comment: 23 pages, 7 figures, accepted by Ap