Thorbergsson, Gudlaugur and Umehara, Masaaki (2012). A refinement of Foreman's four-vertex theorem and its dual version. Kyoto J. Math., 52 (4). S. 743 - 759. DURHAM: DUKE UNIV PRESS. ISSN 2156-2261
Full text not available from this repository.Abstract
A strictly convex curve is a C-infinity-regular simple closed curve whose Euclidean curvature function is positive. Fix a strictly convex curve Gamma, and take two distinct tangent lines l(1) and l(2) of Gamma. A few years ago, Brendan Foreman proved an interesting four-vertex theorem on semiosculating conics of Gamma, which are tangent to l(1) and l(2), as a corollary of Ghys's theorem on diffeomorphisms of S-1. In this paper, we prove a refinement of Foreman's result. We then prove a projectively dual version of our refinement, which is a claim about semiosculating conics passing through two fixed points on Gamma. We also show that the dual version of Foreman's four-vertex theorem is almost equivalent to the Ghys's theorem.
Item Type: | Journal Article | ||||||||||||
Creators: |
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URN: | urn:nbn:de:hbz:38-477079 | ||||||||||||
DOI: | 10.1215/21562261-1728848 | ||||||||||||
Journal or Publication Title: | Kyoto J. Math. | ||||||||||||
Volume: | 52 | ||||||||||||
Number: | 4 | ||||||||||||
Page Range: | S. 743 - 759 | ||||||||||||
Date: | 2012 | ||||||||||||
Publisher: | DUKE UNIV PRESS | ||||||||||||
Place of Publication: | DURHAM | ||||||||||||
ISSN: | 2156-2261 | ||||||||||||
Language: | English | ||||||||||||
Faculty: | Unspecified | ||||||||||||
Divisions: | Unspecified | ||||||||||||
Subjects: | no entry | ||||||||||||
Uncontrolled Keywords: |
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URI: | http://kups.ub.uni-koeln.de/id/eprint/47707 |
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