  We introduce polar metrics on a product manifold, which have product and
warped product metrics as special cases. We prove a de Rham-type theorem
characterizing Riemannian manifolds that can be locally decomposed as a product
manifold endowed with a polar metric. For a product manifold endowed with a
polar metric, our main result gives a complete description of all its isometric
immersions into a space form whose second fundamental forms are adapetd to its
product structure, in the sense that the tangent spaces to each factor are
preserved by all shape operators. This is a far-reaching generalization of a
basic decomposition theorem for isometric immersions of Riemannian products due
to Moore as well as its extension by N\"olker to isometric immersions of warped
products.
