Fukui, Toshizumi; Hasegawa, Masaru; Nakagawa, Kouichi Contact of a regular surface in Euclidean 3-space with cylinders and cubic binary differential equations. (English) Zbl 1371.53004 J. Math. Soc. Japan 69, No. 2, 819-847 (2017). 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. Reviewer: Atsushi Fujioka (Osaka) Cited in 2 Documents MSC: 53A05 Surfaces in Euclidean and related spaces 53A60 Differential geometry of webs 58K05 Critical points of functions and mappings on manifolds Keywords:contact with cylinders; Monge cubic; cylindrical directions PDF BibTeX XML Cite \textit{T. Fukui} et al., J. Math. Soc. Japan 69, No. 2, 819--847 (2017; Zbl 1371.53004) Full Text: DOI Euclid OpenURL