Volume 16, issue 5 (2016)

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Solvable Lie flows of codimension $3$

Naoki Kato

Algebraic & Geometric Topology 16 (2016) 2751–2778
Abstract

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

Keywords
foliations, Lie foliations, homogeneous spaces, solvable Lie algebras, solvable Lie groups
Mathematical Subject Classification 2010
Primary: 57R30
Secondary: 53C12, 22E25