# 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} }

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.

## One Citation

On the min-max width of unit volume three-spheres.

- Mathematics
- 2018

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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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…

On the min-max width of unit volume three-spheres.

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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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