Projective geometry of polygons and discrete 4-vertex and 6-vertex theorems

Details Projective geometry of polygons and discrete 4-vertex and 6-vertex theorems Projective geometry of polygons and discrete 4-vertex and 6-vertex theorems

1999-09-24

arxiv.org/abs/math/9909150v1

Mathematics

Differential Geometry

LaTeX document, 16 pages, 5 figures

Scientific paper

The paper concerns discrete versions of the three well-known results of projective differential geometry: the four vertex theorem, the six affine vertex theorem and the Ghys theorem on four zeroes of the Schwarzian derivative. We study geometry of closed polygonal lines in $\bbRP^d$ and prove that polygons satisfying a certain convexity condition have at least d+1 flattenings. This result provides a new approach to the above mentioned classical theorems.

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