  We study the distribution of projected ellipticity n(epsilon) for galaxies in
a sample of 20 rich (Richness >= 2) nearby (z < 0.1) clusters of galaxies. We
find no evidence of differences in n(epsilon), although the nearest cluster in
the sample (the Coma Cluster) is the largest outlier (P(same) < 0.05). We then
study n(epsilon) within the clusters, and find that epsilon increases with
projected cluster-centric radius R (hereafter the epsilon-R relation). This
trend is preserved at fixed magnitude, showing that this relation exists over
and above the trend of more luminous galaxies to be both rounder and more
common in the centres of clusters. The epsilon-R relation is particularly
strong in the subsample of intrinsically flattened galaxies (epsilon > 0.4),
therefore it is not a consequence of the increasing fraction of round slow
rotator galaxies near cluster centers. Furthermore, the epsilon-R relation
persists for just smooth flattened galaxies and for galaxies with de
Vaucouleurs-like light profiles, suggesting that the variation of the spiral
fraction with radius is not the underlying cause of the trend. We interpret our
findings in light of the classification of early type galaxies (ETGs) as fast
and slow rotators. We conclude that the observed trend of decreasing epsilon
towards the centres of clusters is evidence for physical effects in clusters
causing fast rotator ETGs to have a lower average intrinsic ellipticity near
the centres of rich clusters.
