Four-dimensional, Ricci- at manifolds which admit a metric

Abstract

This paper discusses the relationships between the metric, the connec-
tion and the curvature tensor of 4-dimensional, Ricci at manifolds which
admit a metric. It is shown that these metric and curvature objects are
essentially equivalent conditions for such manifolds if one excludes cer-
tain very special cases and which occur when the signature is indenite.
In a similar vein, some relevant remarks are made regarding the Weyl
conformal tensor.