On projectively related Einstein metrics in Riemann-Finsler geometry

In this paper we study pointwise projectively related Einstein metrics (having the same geodesics as point sets). We show that pointwise projectively related Einstein metrics satisfy a simple equation along geodesics. In particular, we show that if two pointwise projectively related Einstein metrics are complete with negative Einstein constants, then one is a multiple of another. Received: 28 October 1999 / Revised: 10 January 2000 /Published online: 18 June 2001