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

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Masaaki Umehara¹ 

[1] Department of Mathematics, Graduate School of Science, Osaka University

关键词: Sextactic points;    affine curvature;    inflection points;    affine evolute.;   

DOI  :  10.3792/pjaa.87.10

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

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.

【 授权许可】

Unknown