Tree-like curves and their inflection points

Details Tree-like curves and their inflection points Tree-like curves and their inflection points

1997-08-12

arxiv.org/abs/dg-ga/9708009v1

Mathematics

Differential Geometry

AMSTeX-file with 10 pictures enclosed as eps-files, 18 pages, to appear in the AMS-volume on knots and curves, editor S.Tabach

Scientific paper

We give a criterion when a planar tree-like curve, i.e. a generic immersed plane curve each double point of which cuts it into two disjoint parts, can be send by a diffeomorphism of the plane onto a curve with no inflection points. We also present some upper and lower bounds for the minimal number of inflection points on such curves unremovable by diffeomorphisms of the plane in terms of their combinatorics.

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