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 bar{D}-metrics. The non-Riemannian curvatures of R-quadratic Finsler spaces and their special case, the R-quadratic generalized (alpha, beta)-metrics, are analyzed to gain insights into their behavior. The paper then introduces the bar{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.

کلیدواژه ها:

R-quadratic Finsler metrics ، S-curvature ، bar{D}-metrics ، Xi-curvature ، Generalized (alpha ، beta)-metrics.