Algebraic & Geometric Topology

Solvable Lie flows of codimension $3$

Naoki Kato

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Abstract

In Appendix E of Riemannian foliations [Progress in Mathematics 73, Birkhäuser, Boston (1988)], É Ghys proved that any Lie g–flow is homogeneous if g is a nilpotent Lie algebra. In the case where g is solvable, we expect any Lie g–flow to be homogeneous. In this paper, we study this problem in the case where g is a 3–dimensional solvable Lie algebra.

Article information

Source
Algebr. Geom. Topol., Volume 16, Number 5 (2016), 2751-2778.

Dates
Received: 11 February 2015
Revised: 13 November 2015
Accepted: 11 April 2016
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841227

Digital Object Identifier
doi:10.2140/agt.2016.16.2751

Mathematical Reviews number (MathSciNet)
MR3572347

Zentralblatt MATH identifier
1356.57022

Subjects
Primary: 57R30: Foliations; geometric theory
Secondary: 53C12: Foliations (differential geometric aspects) [See also 57R30, 57R32] 22E25: Nilpotent and solvable Lie groups

Keywords
foliations Lie foliations homogeneous spaces solvable Lie algebras solvable Lie groups

Citation

Kato, Naoki. Solvable Lie flows of codimension $3$. Algebr. Geom. Topol. 16 (2016), no. 5, 2751--2778. doi:10.2140/agt.2016.16.2751. https://projecteuclid.org/euclid.agt/1510841227


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