This paper introduces a new quantity in Finsler geometry, called the generalized Berwald projective Weyl ( \(GB\widetilde{W}\) ) metric. The C-projective invariance of these metrics is demonstrated, and it is shown that they constitute a proper subset of the class of generalized Douglas (GDW) metrics. The paper also proves that all GDW metrics with vanishing Landsberg curvature are of R-quadratic type. The class of GDW metrics contains all Finsler metrics of scalar curvature, which provides an extension of the well-known Numata’s theorem.
