Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-K\"ahler Calabi-Yau geometry and pluriclosed flow   Hermitian, pluriclosed metrics with vanishing Bismut-Ricci form give a
natural extension of Calabi-Yau metrics to the setting of complex, non-K\"ahler
manifolds, and arise independently in mathematical physics. We reinterpret this
condition in terms of the Hermitian-Einstein equation on an associated
holomorphic Courant algebroid, and thus refer to solutions as Bismut
Hermitian-Einstein. This implies Mumford-Takemoto slope stability obstructions,
and using these we exhibit infinitely many topologically distinct complex
manifolds in every dimension with vanishing first Chern class which do not
admit Bismut Hermitian-Einstein metrics. This reformulation also leads to a new
description of pluriclosed flow in terms of Hermitian metrics on holomorphic
Courant algebroids, implying new global existence results, in particular on all
complex non-K\"ahler surfaces of nonnegative Kodaira dimension. On complex
manifolds which admit Bismut-flat metrics we show global existence and
convergence of pluriclosed flow to a Bismut-flat metric, which in turn gives a
classification of generalized K\"ahler structures on these spaces.

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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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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: gr-qc