Contact of a regular surface in Euclidean 3-space with cylinders and cubic binary differential equations (Q2360956)

The authors investigate the contact types of a regular surface in the Euclidean \(3\)-space with right circular cylinders by giving the Monge normal form of cylinders. They 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. They also investigate the kernel field of \(A_n\)-contact cylinders on the surface, for \(n\geq 3\), which is defined by a cubic binary differential equation, and classify singularity types of its flow in generic context.