Weakly Douglas Finsler warped product metrics

Recent studies show that warped product manifolds are useful in differential geometry as well as in physics. The goal of this paper is to study on some projective invariants of a special product manifold with Finsler metrics arising from warped products. Firstly, we consider the class of weakly Douglas metrics, weaker notion of Douglas metrics, introduced by Atashafrouz, Najafi and Tayebi in [4]. We prove that every Finsler warped product manifold Mn (n ≥ 3) is weakly Douglas if and only if it is Douglas. Finally, under a certian condition, we show that a class of Finsler warped product metric is locally projectively flat if and only if it is of scalar flag curvature.