Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fano contact manifolds and nilpotent orbits   A contact structure on a complex manifold M is a corank 1 subbundle F of T(M)
such that the bilinear form on F with values in the quotient line bundle
L=T(M)/F deduced from the Lie bracket of vector fields is everywhere
non-degenerate. In this paper we consider the case where M is a Fano manifold;
this implies that L is ample. If g is a simple Lie algebra, the unique closed
orbit in P(g) (for the adjoint action) is a Fano contact manifold; it is
conjectured that every Fano contact manifold is obtained in this way. A
positive answer would imply an analogous result for compact quaternion-Kahler
manifolds with positive scalar curvature, a longstanding question in Riemannian
geometry. In this paper we solve the conjecture under the additional
assumptions that the group of contact automorphisms of M is reductive, and that
the image of the rational map M - - -> P(H0(M,L)*) associated to L has maximum
dimension. The proof relies on the properties of the nilpotent orbits in a
semi-simple Lie algebra, in particular on the work of R. Brylinski and B.
Kostant.

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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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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: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph