Journal article

Geodesic rigidity of conformal connections on surfaces

  • Mettler, Thomas Department of Mathematics, ETH Zürich, Switzerland - Department of Mathematics, University of Fribourg, Switzerland
    23.05.2015
Published in:
  • Mathematische Zeitschrift. - 2015, vol. 281, no. 1-2, p. 379–393
English We show that a conformal connection on a closed oriented surface Σ of negative Euler characteristic preserves precisely one conformal structure and is furthermore uniquely determined by its unparametrised geodesics. As a corollary it follows that the unparametrised geodesics of a Riemannian metric on Σ determine the metric up to constant rescaling. It is also shown that every conformal connection on the 2-sphere lies in a complex 5-manifold of conformal connections, all of which share the same unparametrised geodesics.
Faculty
Faculté des sciences
Department
Département de Mathématiques
Language
  • English
Classification
Mathematics
License
License undefined
Identifiers
Persistent URL
https://folia.unifr.ch/unifr/documents/304462
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