Some non-Riemannian curvature properties of the new class of \((\alpha , \beta )\)-metrics

In this paper, we study some important non-Riemannian curvature properties of the new class of \( (\alpha ,\beta ) \) $(\alpha ,\beta )$ -metrics introduced by Pişcoran–Mishra in Finsler geometry. We prove that this class of Finsler metrics are Landsbergian if and only if they are weakly Landsbergian if and only if they are Berwaldian. Then, we show that this class of Finsler metrics has vanishing \(\Xi \) $\mathrm{\Xi }$ -curvature if and only if they have vanishing S-curvature \(\textbf{S}=0\) $\mathbf{S}=0$ . Finally, we show that this class of Finsler metrics has almost vanishing H-curvature if and only if \(\textbf{H}=0\) $\mathbf{H}=0$ .