Contact of a regular surface in Euclidean 3-space with cylinders and cubic binary differential equations. (English) Zbl 1371.53004

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.


53A05 Surfaces in Euclidean and related spaces
53A60 Differential geometry of webs
58K05 Critical points of functions and mappings on manifolds
Full Text: DOI Euclid