the curvatures of r-quadratic finsler metrics

This paper presents a study of r-quadratic finsler spaces and a new class of finsler metrics called d¯-metrics. the non-riemannian curvatures of r-quadratic finsler spaces and their special case, the r-quadratic generalized (α, β)-metrics, are analyzed to gain insights into their behavior. the paper then introduces the d¯-metrics, which are shown to be a proper subset of the class of gdw-metrics and contain the class of douglas metrics. this paper contributes to the understanding of r-quadratic finsler spaces and their properties, and presents a novel class of finsler metrics with potential applications in the field. msc(2010): 53b40; 53c60