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

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 370卷 / 01期

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

页码：669 / 693

页数：25

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