Disques j-holomorphes contenus dans une hypersurface
DOI:
https://doi.org/10.4067/S0716-09172009000200004Abstract
We study germs of J-Holomorphic curves contained in M, a real analytic hypersurface of an symplectic manifold of dimension 4- We show, under topological hypothesis on M, that if M is compact then M is of finite type and so there is no germs of J-holomorphic curves on M (with J adapted with the symplectic form). In C2 with the standard complex structure, this is a classical result of Diederich-Fornaess.References
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[2] T. Bloom-I. Graham. : A geometric characterization of points of type m on real submanifolds of Cn, J. Diff. Geometry. 12, pp. 171—182, (1977).
[3] B. Deroin. : Surfaces branchées et solénoides e-holomorphes, arXiv. 593, (2004).
[4] Geometry I. : Encyclopaedia of Math.Sciences R. V. Gamkrelidze (Ed), 28 (1991).
[5] H. Goldschmidt. : Integrability criteria for systems of non-linear partial differential equations, J. Diff. Geometry. 1, pp. 269-307, (1967).
[6] M. Gromov. : Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82, pp. 307-347, (1985).
[7] E. Mazzilli. : Germes d’ensembles analytiques dans une hypersurface algèbrique, Ark. Mat. 44, pp. 327-333, (2006).
[8] K. Diederich-J. E. Fornaess. : Pseudoconvex domains with real analytic boundary, Ann. of Maths. 107, pp. 371-384, (1978).
[9] Camacho-Lins neto. : Geometric theory of foliations, Birkhauser, Boston, MA (1985).
How to Cite
[1]
E. Mazzilli, “Disques j-holomorphes contenus dans une hypersurface”, Proyecciones (Antofagasta, On line), vol. 28, no. 2, pp. 141-153, 1.
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