THREE-MANIFOLDS WITH MANY FLAT PLANES

被引:6
作者
Bettiol, Renato G. [1 ]
Schmidt, Benjamin [2 ]
机构
[1] Univ Penn, Dept Math, 209 South 33rd St, Philadelphia, PA 19104 USA
[2] Michigan State Univ, Dept Math, 619 Red Cedar Rd, E Lansing, MI 48824 USA
关键词
RANK-RIGIDITY; RIEMANNIAN-MANIFOLDS; CURVED MANIFOLDS; HYPERBOLIC RANK; SPHERICAL RANK; VECTOR-FIELDS; CURVATURE; SPACES;
D O I
10.1090/tran/6961
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
收藏
页码:669 / 693
页数:25
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