Closed planar curves without inflections

Details Closed planar curves without inflections Closed planar curves without inflections

2011-03-17

arxiv.org/abs/1103.3343v1

Mathematics

Differential Geometry

13pages, 17figures

Scientific paper

We define a computable topological invariant $\mu(\gamma)$ for generic closed planar regular curves $\gamma$, 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 $\mu(\gamma)$ on a given $\gamma$.

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