| 概要 | In 2004, Burslem and Wilkinson proved local rigidity of
real analytic actions of the Baumslag-Solitar group BS(1,k)
on the circle. In particular, the action generated by
projective transformations f(x)=kx and g(x)=x+1 is
locally rigid.
An analog of 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. |