Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local rigidity of Einstein 4-manifolds satisfying a chiral curvature
  condition   Let (M,g) be a compact oriented Einstein 4-manifold. Write R-plus for the
part of the curvature operator of g which acts on self-dual 2-forms. We prove
that if R-plus is negative definite then g is locally rigid: any other Einstein
metric near to g is isometric to it. This is a chiral generalisation of Koiso's
Theorem, which proves local rigidity of Einstein metrics with negative
sectional curvatures. Our hypotheses are roughly one half of Koiso's. Our proof
uses a new variational description of Einstein 4-manifolds, as critical points
of the so-called poure connection action S. The key step in the proof is that
when R-plus is negative definite, the Hessian of S is strictly positive modulo
gauge.

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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin