Towards a local deﬁnition of body in Continuum Mechanics
The purpose of this paper is to introduce the concept of pyramidal manifold, and to demonstrate that it is useful as a model deﬁnition of three-dimensional body. Pyramidal manifolds generalize three-dimensional manifolds with corners and represent an approach to the deﬁnition of body from the point of view of Diﬀerential Geometry, which facilitates the development of the mathematical theory of Continuum Mechanics. Two maps deﬁned on a pyramidal manifold, the degree and the index, are introduced. Both of them are invariant under deformations and allow taking a ﬁrst step towards a classiﬁcation of bodies. The Stokes theorem for bodies is also discussed, and a proof there of is provided by using diﬀerential forms on pyramidal manifolds.