Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric and Extensor Algebras and the Differential Geometry of
  Arbitrary Manifolds   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 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, 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 \slg defined on M
and also introduce the concept a geometric structure (U,gamma,g) for U 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 operators in metric and geometrical structures, like
ordinary and covariant Hodge coderivatives and some duality identities are
exhibit.

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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc