Closed planar curves without inflections

Shuntaro Ohno; Tetsuya Ozawa; Masaaki Umehara

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arXiv · 1103.3343

Closed planar curves without inflections

Shuntaro Ohno·Tetsuya Ozawa·Masaaki Umehara

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Abstract

We define a computable topological invariant $μ(γ)$ for generic closed planar regular curves $γ$, which gives an effective lower bound for the number of inflection points on a given generic closed planar curve. Using it, we classify the topological types of locally convex curves (i.e. closed planar regular curves without inflections) whose numbers of crossings are less than or equal to five. Moreover, we discuss the relationship between the number of double tangents and the invariant $μ(γ)$ on a given $γ$.

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Shuntaro Ohno, Tetsuya Ozawa, Masaaki Umehara. 2011-03-17. Closed planar curves without inflections. https://arxiv.org/abs/1103.3343

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