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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

Citations:

Zbl 1158.53300
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Full Text: DOI Euclid

References:

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