On projective equivalence and pointwise projective relation of Randers metrics
A Randers metric is a Finsler metric of the form \(F(x,\xi )=\sqrt{g_{ij}(x)\xi ^i\xi ^j}+\omega _i(x)\xi ^i\), where \(g_{ij}\) is a Riemannian metric and \(\omega _i\) is a one-form. In this paper the author proves that the projective equivalence of two Randers metrics \(F=\sqrt{g(\xi ,\xi )}+\omega (\xi )\) and \(\overline{F}=\sqrt{\overline{g}(\xi ,\xi )}+\overline{\omega }(\xi ),\) such that at least one of the one-forms \(\omega\) and \(\overline{\omega }\) is not closed, implies that for a certain constant \(C>0\) we have \(g=C^2\overline{g}\) and the form \(\omega -C\overline{\omega }\) is closed. Finally, as an application, the natural generalization of the projective Lichnerowicz-Obata conjecture for Randers metrics is proved.
scientific article; zbMATH DE number 6078198