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arXiv · 1407.4165

Three-manifolds with many flat planes

Renato G. Bettiol·Benjamin Schmidt
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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.

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Renato G. Bettiol, Benjamin Schmidt. 2014-07-15. Three-manifolds with many flat planes. https://doi.org/10.1090/tran/6961

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