On the HN-integration of spatial (integral) derivatives of multivector fields with singularities in RN

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 HN integrability have been defined. Finally, this led naturally to an extension of Cauchy?s residue theorem in M.