Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: p-brane Newton--Cartan Geometry   We provide a formal definition of p-brane Newton--Cartan (pNC) geometry and
establish some foundational results. Our approach is the same followed in the
literature for foundations of Newton--Cartan Gravity. Our results provide
control of aspects of pNC geometry that are otherwise unclear when using the
usual gauge language of non-relativistic theories of gravity. In particular, we
obtain a set of necessary and sufficient conditions that a pNC structure must
satisfy in order to admit torsion-free, compatible affine connections, and
determine the space formed by the latter. Since pNC structures interpolate
between Leibnizian structures for p=0 and Lorentzian structures for p=d-1 (with
d the dimension of the spacetime manifold), the present work also constitutes a
generalisation of results of Newton--Cartan and (pseudo-) Riemannian geometry.

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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat