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TWO REMARKS ON PQε-PROJECTIVITY OF RIEMANNIAN METRICS
Published online by Cambridge University Press: 02 August 2012
Abstract
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.
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- Copyright © Glasgow Mathematical Journal Trust 2012
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