Geodesic
Poisson geometry and deformation quantization near a strictly pseudoconvex boundary
Journal of the European Mathematical Society, Tome 9 (2007) no. 4, pp. 681-704.

Voir la notice de l'article provenant de la source EMS Press

Let X be a complex manifold with strongly pseudoconvex boundary M. If ψ is a defining function for M, then −logψ is plurisubharmonic on a neighborhood of M in X, and the (real) 2-form σ=i∂∂ˉ(−logψ) is a symplectic structure on the complement of M in a neighborhood in X of M; it blows up along M.
DOI : 10.4171/jems/93
Classification : 32-XX, 53-XX, 00-XX
Keywords: Poisson structure, pseudoconvexity, plurisubharmonic function, contact structure, Lie algebroid 
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Eric Leichtnam; Xiang Tang; Alan Weinstein. Poisson geometry and deformation quantization near a strictly pseudoconvex boundary. Journal of the European Mathematical Society, Tome 9 (2007) no. 4, pp. 681-704. doi : 10.4171/jems/93. http://geodesic.mathdoc.fr/articles/10.4171/jems/93/

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