Contraforms on Pseudo-Riemannian Manifolds

Abstract

On the exterior algebra of forms of a pseudo-Riemannian manifold M there acting three notable operators: exterior differential d, the Hodge operator * and the codifferential δ. There are basic in defining the de Rahm cohomology and for the theory of harmonic forms (Hodge theory) . If one considers the spaces of the skewsymmetric contravariant tensor field of type (o, p) for p = 1, 2, ..., dim M, taking their formal sum and a natural wedge product, one obtains again an algebra. This is called sometimes the algebra of p-vectors but we prefer to call it the algebra of contraforms on M, in agreement with the algebra of forms connected with the space of the skewsymmetric covariant tensors.