On the H_N-Integration of Spatial (Integral) Derivatives of Multivector Fields with Singularities in R^N

Abstract

A method of spatial (integral) differentiation of multivector fields in an N-dimensional manifold M , into which a hyper-rectangle [a,b] is mapped by a bijective smooth map r:[a.b]→M, has been introduced. For a class of discontinuous multivector fields a new concept of a residual field as well as the concept of total H_{N} integrability have been defined. Finally, this led naturally to an extension of Cauchy's residue theorem in R^{N}.