Deformations of Lie subgroups

Abstract:

We give rigidity and universality theorems for embedded deformations of Lie subgroups. If $K \subset H \subset G$ are Lie groups, with ${H^1}(K,g/h) = 0$, then for every ${C^\infty }$ deformation of H, a conjugate of K lies in each nearby fiber ${H_s}$. If $H \subset G$ with ${H^2}(H,g/h) = 0$, then there is a universal “weak” analytic deformation of H, whose base space is a manifold with tangent plane canonically identified with $\operatorname {Ker} {\delta ^1}$.