Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Bochner principle and its applications to Fujiki class $\mathcal C$
  manifolds with vanishing first Chern class   We prove a Bochner type vanishing theorem for compact complex manifolds $Y$
in Fujiki class $\mathcal C$, with vanishing first Chern class, that admit a
cohomology class $[\alpha] \in H^{1,1}(Y,\mathbb R)$ which is numerically
effective (nef) and has positive self-intersection (meaning $\int_Y \alpha^n
\,>\, 0$, where $n\,=\,\dim_{\mathbb C} Y$). Using it, we prove that all
holomorphic geometric structures of affine type on such a manifold $Y$ are
locally homogeneous on a non-empty Zariski open subset. Consequently, if the
geometric structure is rigid in the sense of Gromov, then the fundamental group
of $Y$ must be infinite. In the particular case where the geometric structure
is a holomorphic Riemannian metric, we show that the manifold $Y$ admits a
finite unramified cover by a complex torus with the property that the pulled
back holomorphic Riemannian metric on the torus is translation invariant.

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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
3
The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph