Convex projective surfaces with compatible Weyl connection are hyperbolic

DOI10.2140/apde.2020.13.1073OpenAlexW2796702197MaRDI QIDQ780526

Gabriel P. Paternain, Thomas Mettler

Publication date: 15 July 2020

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.04616

zbMATH Keywords

transport equationsenergy identityWeyl connectionsconvex projective structures

Mathematics Subject Classification ID

Projective differential geometry (53A20) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Differentials on Riemann surfaces (30F30) Other partial differential equations of complex analysis in several variables (32W50)

Related Items (7)

DEFORMATIONS OF THE VERONESE EMBEDDING AND FINSLER -SPHERES OF CONSTANT CURVATURE ⋮ Projectively equivalent Finsler metrics on surfaces of negative Euler characteristic ⋮ Vortices over Riemann surfaces and dominated splittings ⋮ Geometric theory of Weyl structures ⋮ The transport Oka-Grauert principle for simple surfaces ⋮ Holomorphic differentials, thermostats and Anosov flows ⋮ Metrisability of projective surfaces and pseudo-holomorphic curves

Cites Work

• Tensor tomography on surfaces
• Geodesic rigidity of conformal connections on surfaces
• Twistor spaces
• Polynomial cubic differentials and convex polygons in the projective plane
• Flat projective structures on surfaces and cubic holomorphic differentials
• On the injectivity of the X-ray transform for Anosov thermostats
• Some inverse spectral results for negatively curved 2-manifolds
• Lie groups and Teichmüller space
• Spectral rigidity of a compact negatively curved manifold
• On deformation boundary rigidity and spectral rigidity of Riemannian surfaces with no focal points.
• Holomorphic differentials, thermostats and Anosov flows
• Metrisability of two-dimensional projective structures
• Minimal Lagrangian connections on compact surfaces
• Spectral rigidity and invariant distributions on Anosov surfaces
• Affine spheres and convex [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /-manifolds]
• Metric with ergodic geodesic flow is completely determined by unparameterized geodesics
• An algorithm based on a sequence of linear complementarity problems applied to a walrasian equilibrium model: An example
• Weyl metrisability of two-dimensional projective structures

This page was built for publication: Convex projective surfaces with compatible Weyl connection are hyperbolic