Two remarks on $P{Q}^{\epsilon }$-projectivity of Riemannian metrics

Abstract

We show that $P{Q}^{\epsilon }$-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 $\epsilon =0$, $P{Q}^{\epsilon }$-projectivity implies projective equivalence.

arXiv comment6 pages, 2 figures

References in corpus (1)

• The only Kähler manifold with degree of mobility $\ge 3$ is $(CP(n),g_{Fubini-Study})$