Revista Matemática Iberoamericana
Full-Text PDF (196 KB) | Metadata | Table of Contents | RMI summary
Published online: 2020-03-20
On the two-systole of real projective spacesLucas Ambrozio and Rafael Montezuma (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