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January 2011 A simplification of the proof of Bol’s conjecture on sextactic points
Masaaki Umehara
Proc. Japan Acad. Ser. A Math. Sci. 87(1): 10-12 (January 2011). DOI: 10.3792/pjaa.87.10

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.

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Masaaki Umehara. "A simplification of the proof of Bol’s conjecture on sextactic points." Proc. Japan Acad. Ser. A Math. Sci. 87 (1) 10 - 12, January 2011. https://doi.org/10.3792/pjaa.87.10

Information

Published: January 2011
First available in Project Euclid: 28 December 2010

zbMATH: 1232.53020
MathSciNet: MR2777231
Digital Object Identifier: 10.3792/pjaa.87.10

Subjects:
Primary: 53A20
Secondary: 53C75

Keywords: affine curvature , affine evolute , inflection points , Sextactic points

Rights: Copyright © 2011 The Japan Academy

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Vol.87 • No. 1 • January 2011
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