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TWO REMARKS ON PQε-PROJECTIVITY OF RIEMANNIAN METRICS

Published online by Cambridge University Press:  02 August 2012

VLADIMIR S. MATVEEV  and
STEFAN ROSEMANN
VLADIMIR S. MATVEEV
Affiliation:
Institute of Mathematics, FSU Jena, Jena 07737, Germany e-mails: vladimir.matveev@uni-jena.de, stefan.rosemann@uni-jena.de
STEFAN ROSEMANN
Affiliation:
Institute of Mathematics, FSU Jena, Jena 07737, Germany e-mails: vladimir.matveev@uni-jena.de, stefan.rosemann@uni-jena.de
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Abstract

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We show that PQε-projectivity of two Riemannian metrics introduced in [15] (P. J. Topalov, Geodesic compatibility and integrability of geodesic flows, J. Math. Phys.44(2) (2003), 913–929.) implies affine equivalence of the metrics unless ε ∈ {0,−1,−3,−5,−7,. . .}. Moreover, we show that for ε=0, PQε-projectivity implies projective equivalence.

Keywords

53B2053B3553C2153C2253C5537J3570H06
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue 1 , January 2013 , pp. 131 - 138
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

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