Differentiation along Multivector Fields

Abstract

The Lie derivation of multivector fields along multivector fields has been introduced by Schouten (see (10, 11)), and studdied for example in (5) and (12). In the present paper we define the Lie derivation of differential forms along multivector fields, and we extend this con- cept to covariant derivation on tangent bundles and vector bundles, and find natural relations between them and other familiar concepts. Also in spinor bundles, we introduce a covariant derivation along multivector fields and call it the Clifford covariant derivation of that spinor bundle, which is related to its structure and has a natural relation to its Dirac operator.