Sturm theory, Ghys theorem on zeroes of the Schwarzian derivative and flattening of Legendrian curves

DOI10.1007/BF01587937zbMath0972.58003arXivdg-ga/9510007MaRDI QIDQ1925100

Valentin Ovsienko, Sergei Tabachnikov

Publication date: 19 July 2001

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/dg-ga/9510007

zbMATH Keywords

Schwarzian derivativeSturm comparison theoremLegendrian curveflattening pointsGhys' theorem

Mathematics Subject Classification ID

Singularities of differentiable mappings in differential topology (57R45) Theory of singularities and catastrophe theory (58K99) Differentiable maps on manifolds (58C25)

Related Items (11)

Symplectically convex and symplectically star-shaped curves: a variational problem ⋮ A four-vertex theorem for frieze patterns? ⋮ A global theory of flexes of periodic functions ⋮ Sturm theory, Ghys theorem on zeroes of the Schwarzian derivative and flattening of Legendrian curves ⋮ Self-Bäcklund curves in centroaffine geometry and Lamé’s equation ⋮ Projective-umbilic points of circular real hypersurfaces in $\mathbb {C}^2$ ⋮ Variations on R. Schwartz's inequality for the Schwarzian derivative ⋮ Dirichlet to Neumann functional and the group of disc's biholomorphic trasformations ⋮ The Virasoro group and Lorentzian surfaces: The hyperboloid of one sheet ⋮ Diffeomorphisms of the circle and hyperbolic curvature ⋮ Lorentzian worldlines and the Schwarzian derivative

Cites Work

• Sturm theory, Ghys theorem on zeroes of the Schwarzian derivative and flattening of Legendrian curves
• Theorem on six vertices of a plane curve via the Sturm theory
• Around four vertices
• The Four-Vertex Theorem Revisited--Two Variations on the Old Theme

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