Classification of spacetimes according to conformal Killing vectors
  Conformal Killing vectors (CKVs) preserve the spacetime metric up to a factor. Homothetic vectors and Killing vectors are special cases of CKVs. Classification of some classes of spacetimes on the basis of CKVs give interesting results showing how homothetic and Killing vectors which form subsets of the set of CKVs can be recovered as a result of the above classification. 
K. Saifullah