## A refinement of Foreman’s four-vertex theorem and its dual version.(English)Zbl 1262.53004

The authors refine B. Foreman’s four-vertex theorem on semi-osculating conics of a strictly convex curve $$\Gamma$$ [Am. Math. Mon. 114, No. 4, 351–356 (2007; Zbl 1158.53300)]. Foreman’s theorem is an application of Ghys’ theorem on diffeomorphisms of $$S^{1}$$. The authors deduce a projectively dual version of their refinement which is a claim about semi-osculating conics passing through two fixed points on $$\Gamma$$.

### MSC:

 53A04 Curves in Euclidean and related spaces 53A20 Projective differential geometry 53C75 Geometric orders, order geometry

### Keywords:

convex curves; four-vertex theorem; semi-osculating conics

Zbl 1158.53300
Full Text:

### References:

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