A simplification of the proof of Bol’s conjecture on sextactic points. (English) Zbl 1232.53020

Sextactic points of a curve in the projective plane are points, where the osculating conic has higher order contact with the curve, that is, contact of multiplicity at least six. Bol’s conjecture [G Bol, Projektive Differentialgeometrie. I. Göttingen, Vandenhoek & Ruprecht (1950; Zbl 0035.23401)] states that a simple closed, not null-homotopic curve has at least three sextactic points. An affirmative answer to the conjecture has been given in [G Thorbergsson, M Umehara, Nagoya Math. J. 167, 55–94 (2002; Zbl 1088.53049)]. The purpose of the paper under review to provide a more elementary proof of the conjecture.


53A20 Projective differential geometry
53A04 Curves in Euclidean and related spaces
53C75 Geometric orders, order geometry
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