Publication: Asymptotically holomorphic embeddings of contact manifolds in projective spaces
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2001
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American Mathematical Society
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This paper discusses the construction of asymptotically holomorphic embeddings of a (2n−1) -dimensional contact manifold into the projective space CP 2n+1 such that the image is weakly dominated by the symplectic form. The proof follows the same lines as in [L. A. Ibort, D. Martínez-Torres and F. Presas, J. Differential Geom. 56 (2000), no. 2, 235–283 ] and most details are to be found in that paper. The asymptotically holomorphic techniques were pioneered in [S. K. Donaldson, J. Differential Geom. 44 (1996), no. 4, 666–705].
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D. Auroux, Symplectic 4-manifolds as branched coverings of CP2. Invent. Math. 139 (2000), 551-602.
D. Borthwick and A. Uribe, Nearly kählerian embeddings of symplectic manifolds. Asian J. Math. 4 (2000), 599-620.
S. K. Donaldson, Symplectic submanifolds and almost-complex geometry. J. Diff. Geom. 44 (1996), 666-705.
Lefschetz pencils on symplectic manifolds. J. Diff. Geom. 53(1999), 205-236.
J. Etnyre, Convexity in contact geometry. Topology Appl. 88 (1998), 3-25.
A. Ibort, D. Martínez and F. Presas, On the construction of contact submanifolds with prescribed topology. To appear in J. Diff. Geom.
V. Muñoz, F. Presas and I. Sols, Almost holomorphic embeddings in grassmannians with applications to singular symplectic submanifolds. math.DG/0002212
F. Presas, Lefschetz type pencils on contact manifolds. math.SG/0007034