Almost flat manifold

In mathematics, a smooth compact manifold M is called almost flat if for any $\varepsilon>0$ there is a Riemannian metric $g_\varepsilon$ on M such that $\mbox{diam}(M,g_\varepsilon)\le 1$ and $g_\varepsilon$ is $\varepsilon$ -flat, i.e. for the sectional curvature of $K_{g_\varepsilon}$ we have $|K_{g_\epsilon}| < \varepsilon$ .

单词	Almost flat manifold
释义	Almost flat manifold 英语百科 Almost flat manifold In mathematics, a smooth compact manifold M is called almost flat if for any $\varepsilon>0$ there is a Riemannian metric $g_\varepsilon$ on M such that $\mbox{diam}(M,g_\varepsilon)\le 1$ and $g_\varepsilon$ is $\varepsilon$ -flat, i.e. for the sectional curvature of $K_{g_\varepsilon}$ we have $\|K_{g_\epsilon}\| < \varepsilon$ .
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