Rigidity of certain solvable actions on the sphere

Abstract

An analog of the Baumslag-Solitar group BS(1,k) naturally acts on the sphere by conformal transformations. The action is not locally rigid in higher dimension, but exhibits a weak form of local rigidity. More precisely, any perturbation preserves a smooth conformal structure.

21 pages, no figures

References in corpus (1)

• $C^1$-actions of Baumslag-Solitar groups on $S^1$

Cited by in corpus (6)

• Rigidity of some abelian-by-cyclic solvable group actions on ${\mathbb{T}}^N$
• Rigidity for $C^1$ actions on the interval arising from hyperbolicity I: solvable groups
• Hyperbolicity as an obstruction to smoothability for one-dimensional actions
• Global Rigidity of Some Abelian-by-Cyclic group actions on $\T^2$
• Local rigidity of certain actions of nilpotent-by-cyclic groups on the sphere
• Local rigidity of certain solvable group actions on tori