Duality and integrability on contact Fano manifolds

Details Duality and integrability on contact Fano manifolds Duality and integrability on contact Fano manifolds

2010-02-03

arxiv.org/abs/1002.0698v1

Mathematics

Algebraic Geometry

Dedicated in memory of Marcin Hauzer. 21 pages

Scientific paper

We address the problem of classification of contact Fano manifolds. It is conjectured that every such manifold is necessarily homogeneous. We prove that the Killing form, the Lie algebra grading and parts of the Lie bracket can be read from geometry of an arbitrary contact manifold. Minimal rational curves on contact manifolds (or contact lines) and their chains are the essential ingredients for our constructions.

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