Necessary and sufficient conditions for n-dimensional conformal Einstein spaces via dimensionally dependent identities -: art. no. 012503

Listing has recently extended results of Kozameh, Newman, and Tod for four-dimensional space-times and presented a set of-necessary and sufficient conditions for a metric to be locally conformally equivalent to an Einstein metric in all semi-Riemannian spaces of dimension n greater than or equal to 4-subject to a nondegeneracy restriction on the Weyl tensor. By exploiting dimensionally dependent identities we demonstrate how to construct two alternative versions of these necessary and sufficient conditions which we believe will be useful in applications. The four-dimensional case is discussed in detail and examples are also given in five and six dimensions. (C) 2005 American Institute of Physics.