On Generalized Einstein Metrics
arXiv:math/0703028
Abstract
Recall that the usual Einstein metrics are those for which the first Ricci contraction of the covariant Riemann curvature tensor is proportional to the metric. Assuming the same type of restrictions but instead on the different contractions of Thorpe tensors, one gets several natural generalizations of Einstein's condition. In this paper, we study some properties of these classes of metrics.
11 pages, new results (theorems 3.3 and 3.4) added and references updated