On the two-systole of real projective spaces

• Lucas Ambrozio ^[1] ; Rafael Montezuma ^[2]
  1. [1] University of Warwick

     University of Warwick

     Reino Unido

     
  2. [2] University of Massachusetts System

     University of Massachusetts System

     City of Boston, Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 36, Nº 7, 2020, págs. 1979-1988
• Idioma: inglés
• DOI: 10.4171/rmi/1188
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• Resumen

  • 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.