CR and Holomorphic Embeddings and Pseudo-conformally Flat Metrics
  We study the non-embddability property for a class of real hypersurfaces, called real hypersurfaces of involution type, into the sphere in the low codimensional case, by making use of property of a naturally related Gauss curvature. We also study rigidity problems for conformal maps between a class of K\"ahler manifolds with pseud-conformally flat metrics. 
Xiaojun Huang, Shanyu Ji and Brandon Lee
math.CV math.DG