We study the distribution of projected ellipticity n ( \epsilon ) for galaxies in a sample of 20 rich ( Richness \geq 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 ( \mathrm { 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 .