A cylinder has 2 flat surfaces and 1 curved surface. In differential geometry, a cylinder is defined more broadly as any ruled surface spanned by a one-parameter family of parallel lines.As such it can have any number of flat surfaces but need not have any at all.A cylinder whose cross section is an ellipse, parabola, or hyperbola is called an elliptic cylinder, parabolic cylinder, or hyperbolic cylinder respectively; these have no flat surfaces.s such it can have any number of flat surfaces but need not have any at all. A cylinder whose cross section is an ellipse, parabola, or hyperbola is called an elliptic cylinder, parabolic cylinder, or hyperbolic cylinder respectively; these have no flat surfaces.