Geometric and Extensor Algebras and the Differential Geometry of Arbitrary Manifolds精品.pdfVIP

7 Geometric and Extensor Algebras and the 0 0 2 Differential Geometry of Arbitrary Manifolds. v o 1 2 1 V. V. Fern´andez ,A. M. Moya and W. A. Rodrigues Jr . N 1 Institute of Mathematics, Statistics and Scientific Computation 9 IMECC-UNICAMP CP 6065 2 13083-859 Campinas, SP, Brazil ] e-mail: walrod@ime.unicamp.br virginvelfe@.ar G 2Department of Mathematics, University of Antofagasta, Antofagasta, Chile D. e-mail: mmoya@uantof.cl h t February 2, 2008 a m [ Abstract 2 v We give in this paper which is the third in a series of four a theory of 4 covariant derivatives of representatives of multivector and extensor fields 9 on an arbitrary open set U ⊂ M , based on the geometric and extensor 0 calculus on an arbitrary smooth manifold M . This is done by introducing 3 the notion of a connection extensor field γ defining a parallelism structure 0 on U ⊂ M , which represents in a well defined way the action on U of 7 the restriction there of some given connection ∇ defined on M . Also we 0 give a novel and intrinsic presentation (i.e., one that does not depend on / h