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HOME > Table of Contents and Abstracts > Vol. 60, No. 2
Tohoku Mathematical Journal
2008
June
SECOND SERIES VOL. 60, NO. 2
Tohoku Math. J.
60 (2008), 149181

Title
INFLECTION POINTS AND DOUBLE TANGENTS ON ANTICONVEX CURVES IN THE REAL PROJECTIVE PLANE
Author
Gudlugur Thorbergsson and Masaaki Umehara
(Received July 5, 2006, revised August 3, 2007) 
Abstract.
A simple closed curve in the real projective plane is called anticonvex if for each point on the curve, there exists a line which is transversal to the curve and meets the curve only at that given point. Our main purpose is to prove an identity for anticonvex curves that relates the number of independent (true) inflection points and the number of independent double tangents on the curve. This formula is a refinement of the classical Möbius theorem. We also show that there are three inflection points on a given anticonvex curve such that the tangent lines at these three inflection points cross the curve only once. Our approach is axiomatic and can be applied in other situations. For example, we prove similar results for curves of constant width as a corollary.
2000 Mathematics Subject Classification.
Primary 53A20; Secondary 53C75.


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