Studies of low surface brightness (LSB) galaxies in nearby clusters have revealed a sub-population of extremely diffuse galaxies with central surface brightness $mu_{0,g}$ > 24 mag arcsec$^{-2}$ and effective radius between 1.5 kpc < R$_{e}$ < 10 kpc. The origin of these Ultra Diffuse Galaxies (UDGs) is still unclear, although several theories have been suggested. We exploit the deep g, r and i-band images of the Fornax Deep Survey (FDS), in order to identify LSB galaxies in the center of the Fornax cluster. We identified visually all extended structures having r-band central surface brightness of $mu_{0,r}$ > 23 mag arcsec$^{-2}$. We classified the objects based on their appearance and performed 2D Sersic model fitting with GALFIT. We analyzed their distribution and orientations in the cluster, and studied their colors and compared the LSB galaxies in Fornax with those in other environments. Our sample consists of 205 galaxies of which 196 are LSB dwarfs (with R$_e$ < 1.5kpc) and nine are UDGs (R$_e$ > 1.5 kpc). We show that the UDGs have g-r colors similar to those of LSB dwarfs. The largest UDGs in our sample appear different from the other LSB galaxies, in that they are significantly more elongated and extended, whereas the smaller UDGs differ from the LSB dwarfs only by their effective radii. We do not find clear differences between the structural parameters of the UDGs in our sample and those of UDGs in other galaxy environments. We find that the dwarf LSB galaxies in our sample are less concentrated in the cluster center than the galaxies with higher surface brightness, and that their number density drops in the core of the cluster. Our findings are consistent with the small UDGs forming the tail of a continuous distribution of less extended LSB galaxies. However, the elongated and distorted shapes of the large UDGs could imply that they are tidally disturbed galaxies.
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