فهرست نشریات علمی دسترسی آزاد ایران

On a real vector space $V$, a Randers norm $\hat{F}$ is defined by $\hat{F}=\hat{\alpha}+\hat{\beta}$, where $\hat{\alpha}$ is a Euclidean norm and $\hat{\beta}$ is a covector. We show that the unit sphere $\Sigma$ in the Randers space $(V,\hat{F})$ has positive flag curvature, if and only if $|\hat{\beta}|_{\hat{\alpha}}< (5-\sqrt{17})/2 \approx 0.43845$, thus answering a problem proposed by Prof. Zhongmin Shen. Moreover, we prove that the flag curvature of $\Sigma$ has a universal lower bound $-4$.