Foliations associated with the structure of a manifold over a Grassmann algebra of even degree exterior forms

Abstract

In this paper we consider a category of manifolds over the algebra of even degree exterior forms on R N. We give examples of suchmanifolds. We explicitly find elements of the pseudogroup of differentiable transformations and demonstrate that on any differentiable manifold there exist affine foliations. © 2012. Allerton Press, Inc.