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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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

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

First available in Project Euclid: 28 December 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Sextactic points affine curvature inflection points affine evolute


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.

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