λ-Projectively Related Finsler Metrics and Finslerian Projective Invariants

In this paper, by using the concept of spherically symmetric metric, we defne the notion of λ-projectively related metrics as an extension of projectively related metrics. We construct some non-trivial examples of λ-projectively related metrics. Let F and G be two λ-projectively related metrics on a manifold M. We find the relation between the geodesics of F and G and prove that any geodesic of F is a multiple of a geodesic of G and the other way around. We prove that the Douglas metrics, Weyl metrics and generalized Douglas-Weyl metrics are λ-projective invariants.