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|Type:||Artigo de periódico|
|Title:||Geometric and extensor algebras and the differential geometry of arbitrary manifolds|
|Abstract:||We give in this paper which is the third in a series of four a theory of covariant derivatives of representatives of multivector and extensor. fields on an arbitrary open set U subset of M, based on the geometric and extensor calculus on an arbitrary smooth manifold M. This is done by introducing the notion of a connection extensor field gamma defining a parallelism structure on U subset of M, which represents in a well-defined way the action on U of the restriction there of some given connection del defined on M. Also we give a novel and intrinsic presentation (i. e. one that does not depend on a chosen orthonormal moving frame) of the torsion and curvature fields of Cartan's theory. Two kinds of Cartan's connection operator fields are identified, and both appear in the intrinsic Cartan's structure equations satisfied by the Cartan's torsion and curvature extensor fields. We introduce moreover a metrical extensor g in U corresponding to the restriction there of given metric tensor g defined on M and also introduce the concept of a geometric structure ( U,gamma, g) for U subset of M and study metric compatibility of covariant derivatives induced by the connection extensor gamma. This permits the presentation of the concept of gauge (deformed) derivatives which satisfy noticeable properties useful in differential geometry and geometrical theories of the gravitational field. Several derivatives of operators in metric and geometrical structures, like ordinary and covariant Hodge co-derivatives and some duality identities are exhibited.|
|Editor:||World Scientific Publ Co Pte Ltd|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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