Three-manifolds with many flat planes
Differential Geometry
2017-12-29 v2 Geometric Topology
Abstract
We discuss the rigidity (or lack thereof) imposed by different notions of having an abundance of zero curvature planes on a complete Riemannian 3-manifold. We prove a rank rigidity theorem for complete 3-manifolds, showing that having higher rank is equivalent to having reducible universal covering. We also study 3-manifolds such that every tangent vector is contained in a flat plane, including examples with irreducible universal covering, and discuss the effect of finite volume and real-analiticity assumptions.
Cite
@article{arxiv.1407.4165,
title = {Three-manifolds with many flat planes},
author = {Renato G. Bettiol and Benjamin Schmidt},
journal= {arXiv preprint arXiv:1407.4165},
year = {2017}
}
Comments
LaTeX2e, 24 pages, 7 figures, revised version. To appear in Trans. Amer. Math. Soc