Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Curvature of quaternionic K\"ahler manifolds with $S^1$-symmetry   We study the behavior of connections and curvature under the HK/QK
correspondence, proving simple formulae expressing the Levi-Civita connection
and Riemann curvature tensor on the quaternionic K\"ahler side in terms of the
initial hyper-K\"ahler data. Our curvature formula refines a well-known
decomposition theorem due to Alekseevsky. As an application, we compute the
norm of the curvature tensor for a series of complete quaternionic K\"ahler
manifolds arising from flat hyper-K\"ahler manifolds. We use this to deduce
that these manifolds are of cohomogeneity one.

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The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
32
The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci