Journal of the
Korean Mathematical Society JKMS

A characterization of the $C$-projective vector fields on a Randers space is presented in terms of ${\bf\Xi}$-curvature. It is proved that the ${\bf\Xi}$-curvature is invariant for $C$-projective vector fields. The dimension of the algebra of the $C$-projective vector fields on an $n$-dimensional Randers space is at most $n(n+2)$. The generalized Funk metrics on the $n$-dimensional Euclidean unit ball $\mathbb{B}^n(1)$ are shown to be explicit examples of the Randers metrics with a $C$-projective algebra of maximum dimension $n(n+2)$. Then, it is also proved that an $n$-dimensional Randers space has a $C$-projective algebra of maximum dimension $n(n+2)$ if and only if it is locally Minkowskian or (up to re-scaling) locally isometric to the generalized Funk metric. A new projective invariant is also introduced.

Keywords: Randers metric, projective vector field, ${\bf S}$-curvature, ${\bf \Xi}$-curvature

MSC numbers: Primary 53C60; Secondary 58B40