Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: General Construction of Tubular Geometry   We consider the problem of locally describing tubular geometry around a
submanifold embedded in a (pseudo)Riemannian manifold in its general form.
Given the geometry of ambient space in an arbitrary coordinate system and
equations determining the submanifold in the same system, we compute the
tubular expansion coefficients in terms of this {\it a priori data}. This is
done by using an indirect method that crucially applies the tubular expansion
theorem for vielbein previously derived. With an explicit construction
involving the relevant coordinate and non-coordinate frames we verify
consistency of the whole method up to quadratic order in vielbein expansion.
Furthermore, we perform certain (long and tedious) higher order computation
which verifies the first non-trivial spin connection term in the expansion for
the first time. Earlier a similar method was used to compute tubular geometry
in loop space. We explain this work in the light of our general construction.

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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: math
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph