Contact of circles with surfaces: answers to a question of Montaldi. (English) Zbl 1533.53008
It is stated on page 118 in [J. A. Montaldi, J. Differ. Geom. 23, 109–126 (1986; Zbl 0579.53004)] that an upper bound on the number of circles which can have at least 5-point contact with a generic surface at any point is \(10.\) In the short note the authors show that examples realising this upper bound do exist.
Reviewer: Hans-Bert Rademacher (Leipzig)
MSC:
53A05 | Surfaces in Euclidean and related spaces |
57R45 | Singularities of differentiable mappings in differential topology |
58K05 | Critical points of functions and mappings on manifolds |