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Bounded distance geodesic foliations in Riemannian planes
- Publication Year :
- 2020
-
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.
- Subjects :
- Mathematics - Differential Geometry
53C20 (Primary), 53C22
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2012.09871
- Document Type :
- Working Paper