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Revista Matemática Iberoamericana


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Volume 36, Issue 7, 2020, pp. 1979–1988
DOI: 10.4171/rmi/1188

Published online: 2020-03-20

On the two-systole of real projective spaces

Lucas Ambrozio[1] and Rafael Montezuma[2]

(1) University of Warwick, Coventry, UK
(2) University of Massachusetts, Amherst, USA and Universidade Federal do Ceará, Fortaleza, Brazil

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.

Keywords: Two-systole, minimal two-spheres, homogeneous three-spheres, integral-geometric formula

Ambrozio Lucas, Montezuma Rafael: On the two-systole of real projective spaces. Rev. Mat. Iberoam. 36 (2020), 1979-1988. doi: 10.4171/rmi/1188