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

摘要

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)-ramtact 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.