Cylindrical perspective is a form of distortion caused by fisheye and panoramic lenses which reproduce straight horizontal lines above and below the lens axis level as curved while reproducing straight horizontal lines on lens axis level as straight. This is also a common feature of wide-angle anamorphic lenses of less than 40mm focal length in cinematography.
Essentially it is just barrel distortion but only in the horizontal plane. It is an artifact of the squeezing process that anamorphic lenses do to fit widescreen images onto standard-width film.
References
Cylindrical perspective Wikipedia(Text) CC BY-SA