Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Riemannian Metrics on Locally Projectively Flat Manifolds   The expression (-1/u) times the Hessian of u transforms as a symmetric (0,2)
tensor under projective coordinate transformations, so long as u transforms as
a section of a certain line bundle. On a locally projectively flat manifold M,
the section u can be regarded as a metric potential analogous to the local
potential in Kahler geometry. If M is compact and u is a negative section of
the dual of the tautological bundle whose Hessian is positive definite, then M
is projectively equivalent to a quotient of a bounded convex domain in R^n. The
same is true if M has a boundary on which u=0. This theorem is analogous to a
result of Schoen and Yau in locally conformally flat geometry. The proof uses
affine differential geometry techniques developed by Cheng and Yau.

31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
1
The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin