Rigidity of compact pseudo-Riemannian homogeneous spaces for solvable Lie groups

Abstract

Let $M$ be a compact connected pseudo-Riemannian manifold on which a solvable connected Lie group $G$ of isometries acts transitively. We show that $G$ acts almost freely on $M$ and that the metric on $M$ is induced by a bi-invariant pseudo-Riemannian metric on $G$. Furthermore, we show that the identity component of the isometry group of $M$ coincides with $G$.

References in corpus (2)

• Deformations and rigidity of lattices in solvable Lie groups
• On the Koszul map of Lie algebras

Cited by in corpus (6)

• Isometry Lie algebras of indefinite homogeneous spaces of finite volume
• Compact pseudo-Riemannian homogeneous Einstein manifolds of low dimension
• Uniqueness of ad-invariant metrics
• Rigidity of pseudo-Hermitian homogeneous spaces of finite volume
• Lattices in the four-dimensional split oscillator group
• Simply connected indefinite homogeneous spaces of finite volume