Three-manifolds with many flat planes

Renato G. Bettiol, Benjamin Schmidt

Research output: Research - peer-reviewArticle

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-analyticity assumptions.

LanguageEnglish (US)
Pages669-693
Number of pages25
JournalTransactions of the American Mathematical Society
Volume370
Issue number1
DOIs
StatePublished - Jan 1 2018

Profile

Three-manifolds
Rigidity
Covering
Tangent vector
Analyticity
Finite Volume
Curvature
Zero
Theorem

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Three-manifolds with many flat planes. / Bettiol, Renato G.; Schmidt, Benjamin.

In: Transactions of the American Mathematical Society, Vol. 370, No. 1, 01.01.2018, p. 669-693.

Research output: Research - peer-reviewArticle

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