Closed planar curves without inflections
Authors:
Shuntaro Ohno, Tetsuya Ozawa and Masaaki Umehara
Journal:
Proc. Amer. Math. Soc. 141 (2013), 651665
MSC (2010):
Primary 53A04; Secondary 53A15, 53C42
Published electronically:
June 1, 2012
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Abstract: We define a computable topological invariant for generic closed planar regular curves , 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 of a given .
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Additional Information
Shuntaro Ohno
Affiliation:
Department of Mathematics, Kyoto Koka Senior High School, Nishikyogoku Nodacho, Kyoto 6150861, Japan
Email:
tkmskr0329@yahoo.co.jp
Tetsuya Ozawa
Affiliation:
Department of Mathematics, Meijo University, Tempaku, Nagoya, 4688502 Japan
Email:
ozawa@meijou.ac.jp
Masaaki Umehara
Affiliation:
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2121W834, Ookayama Meguroku, Tokyo 1528552, Japan
Email:
umehara@is.titech.ac.jp
DOI:
http://dx.doi.org/10.1090/S00029939201211319X
PII:
S 00029939(2012)11319X
Keywords:
Plane curve,
inflection point,
double tangent
Received by editor(s):
December 21, 2010
Received by editor(s) in revised form:
June 21, 2011, and June 26, 2011
Published electronically:
June 1, 2012
Additional Notes:
The third author was partially supported by the GrantinAid for Scientific Research (A) No. 22244006, Japan Society for the Promotion of Science.
Communicated by:
Daniel Ruberman
Article copyright:
© Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
