Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hermitian Structures and Compatible Connections on A-bundles   A-manifolds and A-bundles are manifolds and vector bundles modelled on a
projective finitely generated module over a topological algebra A. In this
paper we investigate the conditions under which an A-bundle is provided with an
A-valued hermitian structure and a compatible connection, in case A is a
commutative complete locally m-convex C*-algebra with unit. In this
investigation two obstacles appear: first, A-manifolds do not admit partitions
of unity in the classical sence, and, secondly, the existence of a hermitian
structure is not equivalent to the reduction of the structural group of the
bundle to a certain subgroup. However, we prove that if the bundle has a
trivializing covering whose transition functions take values in the group of
the "A-hermitian product preserving" automorphisms of the fibre type and the
base space admits at least one A-valued partition of unity (subordinate to this
covering), then the A-bundle admits an A-hermitian structure and a compatible
connection.

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The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio