Besse projective spaces with many diameters
Differential Geometry
2023-06-13 v2
Abstract
It is known that Blaschke manifolds (where injectivity radius equals diameter) are Besse manifolds (where all geodesics are closed). We show that Besse manifolds with sufficiently many diameter realizing directions are Blaschke. We also provide bounds in terms of diameter on the length of the shortest closed geodesic for pinched curvature metrics on simply connected manifolds.
Cite
@article{arxiv.2201.03676,
title = {Besse projective spaces with many diameters},
author = {Ian Adelstein and Franco Vargas Pallete},
journal= {arXiv preprint arXiv:2201.03676},
year = {2023}
}
Comments
7 pages, to appear in The Journal of Geometric Analysis. Comments are welcome