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