Bounded distance geodesic foliations in Riemannian planes
Differential Geometry
2020-12-21 v1
Abstract
A conjecture of Burns and Knieper asks whether a 2-plane with a metric without conjugate points, and with a geodesic foliation whose lines are at bounded Hausdorff distance, is necessarily flat. We prove this conjecture in two cases: under the hypothesis that the plane admits total curvature, and under the hypothesis of visibility at some point. Along the way, we show that all geodesic line foliations on a Riemannian 2-plane must be homeomorphic to the standard one.
Cite
@article{arxiv.2012.09871,
title = {Bounded distance geodesic foliations in Riemannian planes},
author = {Jian Ge and Luis Guijarro},
journal= {arXiv preprint arXiv:2012.09871},
year = {2020}
}