On the two-systole of real projective spaces

2018/09/10 by Ambrozio, Lucas, Montezuma, Rafael · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.03636

Abstract

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.

Cited by

• Minimal equators and homological systoles in Berger projective spaces

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