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Local normal forms for geodesically equivalent pseudo-Riemannian metrics


Authors: Alexey V. Bolsinov and Vladimir S. Matveev
Journal: Trans. Amer. Math. Soc. 367 (2015), 6719-6749
MSC (2010): Primary 53B30; Secondary 53C50
DOI: https://doi.org/10.1090/S0002-9947-2014-06416-7
Published electronically: December 10, 2014
MathSciNet review: 3356952
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Abstract: Two pseudo-Riemannian metrics $ g $ and $ \bar g$ are geodesically equivalent if they share the same (unparameterized) geodesics. We give a complete local description of such metrics which solves the natural generalisation of the Beltrami problem for pseudo-Riemannian metrics.


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Additional Information

Alexey V. Bolsinov
Affiliation: School of Mathematics, Loughborough University, Loughborough, LE11 3TU, United Kingdom
Email: A.Bolsinov@lboro.ac.uk

Vladimir S. Matveev
Affiliation: Institute of Mathematics, Friedrich-Schiller University Jena, 07737, Jena, Germany
Email: vladimir.s.matveev@gmail.com

DOI: https://doi.org/10.1090/S0002-9947-2014-06416-7
Received by editor(s): January 22, 2013
Received by editor(s) in revised form: October 25, 2013, and February 28, 2014
Published electronically: December 10, 2014
Additional Notes: The first author was partially supported by Ministry of Education and Science of the Russian Federation (14.B37.21.1935)
The second author was partially supported by DFG (GK 1523) and DAAD (Programm Ostpartnerschaft)
Article copyright: © Copyright 2014 American Mathematical Society