Geodesic Equivalence via Integrability |
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Authors: | Peter Topalov Vladimir S Matveev |
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Institution: | (1) Instut fur Mathematik, Universitat Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland;(2) Institute of Mathematics, BAS, Acad, G.Bonchev Str., bl.8, Sofia, 1113, Bulgaria;(3) Mathematisches Institut, Universität Freiburg, Eckerstr. 1, Germany |
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Abstract: | We suggest a construction that, given an orbital diffeomorphism between two Hamiltonian systems, produces integrals of them. We treat geodesic equivalence of metrics as the main example of it. In this case, the integrals commute; they are functionally independent if the eigenvalues of the tensor g
i g¯ j
are all different; if the eigenvalues are all different at least at one point then they are all different at almost each point and the geodesic flows of the metrics are Liouville integrable. This gives us topological obstacles to geodesic equivalence. |
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Keywords: | geodesically equivalent metrics integrable systems Levi-Civita coordinates projectively equivalent metrics |
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