We establish an integral-geometric formula for minimal two-spheres inside homogeneous three-spheres, and use it to provide a characterisation of each homogeneous metric on the three-dimensional real projective space as the unique metric with the largest possible two-systole among metrics with the same volume in its conformal class.

中文翻译：

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关于实射影空间的两收缩

我们建立了齐次三球体内最小两个球的积分几何公式，并使用它来表征三维真实投影空间上的每个齐次度量，作为唯一的度量，其中度量中最大的两个收缩在其保形类中具有相同的体积。