Proceedings of the Japan Academy, Series A, Mathematical Sciences

A simplification of the proof of Bol’s conjecture on sextactic points

Masaaki Umehara

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Abstract

In a previous work with Thorbergsson, it was proved that a simple closed curve in the real projective plane $\mathbf{P}^{2}$ that is not null-homotopic has at least three sextactic points. This assertion was conjectured by Gerrit Bol. That proof used an axiomatic approach called ‘intrinsic conic system’. The purpose of this paper is to give a more elementary proof.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 87, Number 1 (2011), 10-12.

Dates
First available in Project Euclid: 28 December 2010

Permanent link to this document
https://projecteuclid.org/euclid.pja/1293500472

Digital Object Identifier
doi:10.3792/pjaa.87.10

Mathematical Reviews number (MathSciNet)
MR2777231

Zentralblatt MATH identifier
1232.53020

Subjects
Primary: 53A20: Projective differential geometry
Secondary: 53C75: Geometric orders, order geometry [See also 51Lxx]

Keywords
Sextactic points affine curvature inflection points affine evolute

Citation

Umehara, Masaaki. A simplification of the proof of Bol’s conjecture on sextactic points. Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 1, 10--12. doi:10.3792/pjaa.87.10. https://projecteuclid.org/euclid.pja/1293500472


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