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In this paper, we study a class of Finsler metrics called general $$(\alpha ,\beta )$$ -metrics, which are defined by a Riemannian metric and a 1-form. These metrics form a rich class of Finsler metrics. Suppose that $$F=\alpha \phi (b^{2},s)$$ is a general $$(\alpha ,\beta )$$ -metric which is conformally related to $$\tilde{F}=e^{\sigma (x)}F,$$ where $$\sigma := \sigma (x)$$ is a scalar function on M. We show that if F is Douglas metric, then $$\tilde{F}$$ is also Douglas metric if and only if the conformal transformation is a homothety under suitable condition on $$\phi $$ . Furthermore, we have investigated the conformal transformation of isotropic S-curvature general $$(\alpha ,\beta )$$ -metrics.

Finsler metrics of quadratic curvatures form a rich and important class of metrics. In this paper, we study spherically symmetric metrics of quadratic curvatures. We find equations that characterize R-quadratic spherically symmetric Finsler metrics. In addition, we find the necessary and sufficient conditions for the metrics to be W-quadratic and Ricci-quadratic types.