Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diffeological Levi-Civita connections   A diffeological connection on a diffeological vector pseudo-bundle is defined
just the usual one on a smooth vector bundle; this is possible to do, because
there is a standard diffeological counterpart of the cotangent bundle. On the
other hand, there is not yet a standard theory of tangent bundles, although
there are many suggested and promising versions, such as that of the internal
tangent bundle, so the abstract notion of a connection on a diffeological
vector pseudo-bundle does not automatically provide a counterpart notion for
Levi-Civita connections. In this paper we consider the dual of the
just-mentioned counterpart of the cotangent bundle in place of the tangent
bundle (without making any claim about its geometrical meaning). To it, the
notions of compatibility with a pseudo-metric and symmetricity can be easily
extended, and therefore the notion of a Levi-Civita connection makes sense as
well. In the case when $\Lambda^1(X)$, the counterpart of the cotangent bundle,
is finite-dimensional, there is an equivalent Levi-Civita connection on it as
well.

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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: gr-qc