  A theorem of differential geometry is employed to locally embed a wide class
of superstring backgrounds that admit a covariantly constant null Killing
vector field in eleven-dimensional, Ricci-flat spaces. Included in this class
are exact type IIB superstring backgrounds with non-trivial Ramond-Ramond
fields and a class of supersymmetric string waves. The embedding spaces
represent exact solutions to eleven-dimensional, vacuum Einstein gravity. A
solution of eleven-dimensional supergravity is also embedded in a
twelve--dimensional, Ricci-flat space.
