  We define a Weyl-type curvature tensor that provides a characterisation for
Finsler metrics of constant flag curvature. When the Finsler metric reduces to
a Riemannian metric, the Weyl-type curvature tensor reduces to the classic
projective Weyl tensor. In the general case, the Weyl-type curvature tensor
differs from the Weyl projective curvature, it is not a projective invariant,
and hence Beltrami Theorem does not work in Finsler geometry. We provide the
relation between the Weyl-type curvature tensors of two projectively related
Finsler metrics. Using this formula we show that a projective deformation
preserves the property of having constant flag curvature if and only if the
projective factor is a Hamel function. This way we provide a Finslerian version
of Beltrami Theorem.
