Beyond the generalized Douglas--Weyl spaces

This paper gives new insights into the class of {\it generalized Douglas--Weyl} ($GDW$-) metrics. This projective invariant class of Finsler metrics contains some well-known Finsler metrics such as Douglas, Weyl and $R$-quadratic metrics. Here, some new subclasses of $GDW$-metrics are constructed and considered as the explicit Finsler metrics. Many illustrative and interesting examples are presented.