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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.
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Lucas Ambrozio, Rafael Montezuma, On the two-systole of real projective spaces. Rev. Mat. Iberoam. 36 (2020), no. 7, pp. 1979–1988DOI 10.4171/RMI/1188