English

On the two-systole of real projective spaces

Differential Geometry 2018-10-25 v2

Abstract

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

Cite

@article{arxiv.1809.03636,
  title  = {On the two-systole of real projective spaces},
  author = {Lucas Ambrozio and Rafael Montezuma},
  journal= {arXiv preprint arXiv:1809.03636},
  year   = {2018}
}

Comments

10 pages. Minor typos corrected, keywords added. Submitted version