Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: SU(4)-holonomy via the left-invariant hypo and Hitchin flow   The Hitchin flow constructs eight-dimensional Riemannian manifolds (M,g) with
holonomy in Spin(7) starting with a cocalibrated G_2-structure on a
seven-dimensional manifold. As Sp(2)\subseteq SU(4)\subseteq Spin(7), one may
also obtain Calabi-Yau fourfolds or hyperK\"ahler manifolds via the Hitchin
flow.
  In this paper, we show that the Hitchin flow on almost Abelian Lie algebras
and on Lie algebras with one-dimensional commutator always yields Riemannian
metrics with Hol(g)\subseteq SU(4) but Hol(g)\neq Sp(2). We investigate when we
actually get Hol(g)=SU(4) and obtain so many new explicit examples of
Calabi-Yau fourfolds. The results rely on the connection between cocalibrated
G_2-structures and hypo SU(3)-structures and between the Hitchin and the hypo
flow and on a systematic study of hypo SU(3)-structures and the hypo flow on
Lie algebras. This study gives us many other interesting results: We obtain
full classifications of hypo SU(3)-structures with particular intrinsic torsion
on Lie algebras. Moreover, we can exclude reducible or Sp(2)-holonomy or do get
Hol(g)=SU(4) for the Riemannian manifolds obtained by the hypo flow with
initial values in some other intrinsic torsion classes.

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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: q-bio