Chern-Moser-Weyl Tensor and Embeddings into Hyperquadrics
  The first part of the article surveys some work on the Chern-Moser-Weyl tensor and its application in the embeddability problem into hyperquadrics. In the last section, we give a negative answer to a folklore conjecture concerning the embeddability of compact, strongly pseudoconvex, real algebraic hypersurfaces into a sphere of sufficiently high dimension. 
Xiaojun Huang and Ming Xiao
math.CV