Contact of a regular surface in Euclidean 3-space with cylinders and cubic binary differential equations

We investigate the contact types of a regular surface in the Euclidean 3-space R-3 with right circular cylinders. We present the conditions for existence of cylinders with A(1), A(2), A(3), A(4), A(5),D-4 and D-5 contacts with a given surface. We also investigate the kernel field of A >= 3-contact cylinders on the surface. This is defined by a cubic binary differential equation and we classify singularity types of its flow in the generic context.