Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Riemann curvature tensor on ${\sf RCD}$ spaces and possible applications   We show that on every ${\sf RCD}$ spaces it is possible to introduce, by a
distributional-like approach, a Riemann curvature tensor.
  Since after the works of Petrunin and Zhang-Zhu we know that finite
dimensional Alexandrov spaces are ${\sf RCD}$ spaces, our construction applies
in particular to the Alexandrov setting. We conjecture that an ${\sf RCD}$
space is Alexandrov if and only if the sectional curvature - defined in terms
of such abstract Riemann tensor - is bounded from below.

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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin