  We give several equivalent conditions that characterize the 2+2 warped
spacetimes: imposing the existence of a Killing-Yano tensor $A$ subject to
complementary algebraic restrictions; in terms of the projector $v$ (or of the
canonical 2-form $U$) associated with the 2-planes of the warped product. These
planes are principal planes of the Weyl and/or Ricci tensors and can be
explicitly obtained from them. Therefore, we obtain the necessary and
sufficient (local) conditions for a metric tensor to be a 2+2 warped product.
These conditions exclusively involve explicit concomitants of the Riemann
tensor. We present a similar analysis for the conformally 2+2 product
spacetimes and give an invariant classification of them. The warped products
correspond to two of these invariant classes. The more degenerate class is the
set of product metrics which are also studied from an invariant point of view.
