
## 1. CR automorphisms

1. #### Problem 1.1.

[V. Matveev] Are there nonspherical, compact, nondegenerate CR manifolds which admit essential conformal vector fields?
1. Remark. For strictly pseudoconvex CR manifolds, Schoen proved that the answer is "no"
• Remark. For the analogous problem in Riemannian geometry, C. Frances showed that the answer is "yes" in signature $(n-2,2)$. One might start by trying to adapt his example to the CR setting.

Cite this as: AimPL: Analysis and geometry on pseudohermitian manifolds, available at http://aimpl.org/pshermitian.