# On the two-systole of real projective spaces

@article{Ambrozio2018OnTT,
title={On the two-systole of real projective spaces},
author={Lucas C. Ambrozio and Rafael Montezuma},
journal={arXiv: Differential Geometry},
year={2018}
}
• Published 10 September 2018
• Mathematics
• arXiv: Differential Geometry
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.
1 Citations
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How large can be the width of Riemannian three-spheres of the same volume in the same conformal class? If a maximum value is attained, how does a maximising metric look like? What happens as the

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