Subspace foliations and collapse of closed flat manifolds

被引：0

作者：

Bettiol, Renato G. ^{[1
,2
]}

Derdzinski, Andrzej ^{[3
]}

Mossa, Roberto ^{[4
]}

Piccione, Paolo ^{[4
]}

机构：

[1] CUNY, Lehman Coll, Dept Math, 250 Bedford Pk Blvd W, Bronx, NY 10468 USA

[2] CUNY, Grad Ctr, New York, NY USA

[3] Ohio State Univ, Dept Math, 231 W 18th Ave, Columbus, OH 43210 USA

[4] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo, SP, Brazil

来源：

MATHEMATISCHE NACHRICHTEN | 2022年 / 295卷 / 12期

基金：

美国国家科学基金会;

关键词：

Bieberbach group; collapse; crystallographic group; flat manifold; flat orbifold; foliation; Gromov-Hausdorff convergence; RIEMANNIAN-MANIFOLDS;

D O I：

10.1002/mana.202000156

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study relations between certain totally geodesic foliations of a closed flat manifold and its collapsed Gromov-Hausdorff limits. Our main results explicitly identify such collapsed limits as flat orbifolds, and provide algebraic and geometric criteria to determine whether they are singular.

引用

页码：2338 / 2356

页数：19

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