Flag curvatures of the unit sphere in a Minkowski-Randers space

	Flag curvatures of the unit sphere in a Minkowski-Randers space
AUT Journal of Mathematics and Computing
دوره 2، شماره 2، آذر 2021، صفحه 275-282 اصل مقاله (315.15 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22060/ajmc.2021.20237.1061
نویسندگان
Libing Huang^* ؛ Haibin Su
School of Mathematical Sciences, Nankai University, 94 Weijin Road, Tianjin 300071, P. R. China
چکیده
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 $-4$.
کلیدواژه‌ها
Flag curvature؛ Randers metric؛ Riemannian metric
مراجع

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