Geodesic
Duality and integrability on contact Fano manifolds
Documenta mathematica, Tome 15 (2010), pp. 821-841

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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.
DOI : 10.4171/dm/315
Classification : 14J45, 14M17, 14M20, 53C26
Mots-clés : minimal rational curves, complex contact manifold, Fano variety, adjoint variety, Killing form, Lie bracket, Lie algebra grading 
Jaroslaw Buczynski. Duality and integrability on contact Fano manifolds. Documenta mathematica, Tome 15 (2010), pp. 821-841. doi: 10.4171/dm/315
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     author = {Jaroslaw Buczynski},
     title = {Duality and integrability on contact {Fano} manifolds},
     journal = {Documenta mathematica},
     pages = {821--841},
     year = {2010},
     volume = {15},
     doi = {10.4171/dm/315},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/315/}
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