Lie groupoids and semi-local models of singular Riemannian foliations

被引：0
|
作者：
Alexandrino, Marcos M. [1 ]
Inagaki, Marcelo K. [1 ]
de Melo, Mateus [1 ]
Struchiner, Ivan [1 ]
机构：
[1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, Brazil
来源：
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2022年 / 61卷 / 03期
基金：
巴西圣保罗研究基金会;
关键词：
Singular Riemannian foliation; Lie groupoids; Linearization; Molino's conjecture; INTEGRABILITY; THEOREM;
D O I：
10.1007/s10455-021-09813-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We describe a local model for any singular Riemannian foliation in a neighborhood of a closed saturated submanifold of a singular stratum. Moreover, we construct a Lie groupoid that controls the transverse geometry of the linear approximation of the singular Riemannian foliation around these submanifolds. We also discuss the closure of this Lie groupoid and its Lie algebroid.
引用
收藏
页码：593 / 619
页数：27
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