Examples of open manifolds with positive Ricci curvature and non-proper Busemann functions
Differential Geometry
2023-09-06 v2
Abstract
We give the first example of an open manifold with positive Ricci curvature and a non-proper Busemann function at a point. This provides counterexamples to a longtime well-known open question whether the Busemann function at a point of an open manifold with nonnegative Ricci curvature is proper.
Keywords
Cite
@article{arxiv.2203.15211,
title = {Examples of open manifolds with positive Ricci curvature and non-proper Busemann functions},
author = {Jiayin Pan and Guofang Wei},
journal= {arXiv preprint arXiv:2203.15211},
year = {2023}
}
Comments
Added some discussions on the Busemann functions defined by geodesic spheres