Geodesic rigidity of conformal connections on surfaces
- Mettler, Thomas Department of Mathematics, ETH Zürich, Switzerland - Department of Mathematics, University of Fribourg, Switzerland
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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 et de médecine
- Department
- Département de Mathématiques
- Language
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 257248
- DOI 10.1007/s00209-015-1489-5
- Persistent URL
- https://folia.unifr.ch/unifr/documents/304462
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