We prove that the Fibonacci group F⁢(2,n){F(2,n)} for n odd and n≥11{n\geq 11} is hyperbolic. We do this by applying a curvature argument to an arbitrary van Kampen diagram of F⁢(2,n){F(2,n)} and show that it satisfies a linear isoperimetric inequality. It then follows that F⁢(2,n){F(2,n)} is hyperbolic.

中文翻译：

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斐波那契群𝐹（2，𝑛）对于𝑛奇数和𝑛≥11是双曲的

我们证明对于n个奇数和n≥11{n \ geq 11}的斐波那契群F⁢（2，n）{F（2，n）}是双曲线的。我们通过对F⁢（2，n）{F（2，n）}的任意van Kampen图应用曲率参数来做到这一点，并证明它满足线性等距不等式。然后得出F⁢（2，n）{F（2，n）}是双曲线的。