Generalized Berwald Projective Weyl (GBW~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$GB\widetilde{W}$$\end{document}) Metrics

This paper introduces a new quantity in Finsler geometry, called the generalized Berwald projective Weyl (GBW~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$GB\widetilde{W}$$\end{document}) 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.