Two remarks on $PQ^ε$-projectivity of Riemannian metrics

Details Two remarks on $PQ^ε$-projectivity of Riemannian metrics Two remarks on $PQ^ε$-projectivity of Riemannian metrics

2011-08-15

arxiv.org/abs/1108.2965v1

Mathematics

Differential Geometry

6 pages, 2 figures

Scientific paper

We show that $PQ^{\epsilon}$-projectivity of two Riemannian metrics
introduced in \cite{Top2003} implies affine equivalence of the metrics unless
$\epsilon\in\{0,-1,-3,-5,-7,...\}$. Moreover, we show that for $\epsilon=0$,
$PQ^{\epsilon}$-projectivity implies projective equivalence.

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