The notion of 2-calibrated structure, generalizing contact structures, smooth taut foliations, etc., is defined. Approximately holomorphic geometry as introduced by S. Donaldson for symplectic manifolds is extended to 2-calibrated manifolds. An estimated transversality result that enables to study the geometry of such manifolds is presented.
On définit la notion de structure 2-calibrée, qui généralise celle de structure de contact, feuilletage tendu différentiable, etc. La géométrie approximativement holomorphe, introduite par S. Donaldson pour les variétés symplectiques est généralisée pour les variétés 2-calibrées. On démontre aussi un résultat de transversalité quantitative qui permet d'étudier la géométrie de ces variétés.
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Alberto Ibort 1; David Martínez Torres 1
@article{CRMATH_2004__338_9_709_0, author = {Alberto Ibort and David Mart{\'\i}nez Torres}, title = {Approximately holomorphic geometry and estimated transversality on 2-calibrated manifolds}, journal = {Comptes Rendus. Math\'ematique}, pages = {709--712}, publisher = {Elsevier}, volume = {338}, number = {9}, year = {2004}, doi = {10.1016/j.crma.2004.03.003}, language = {en}, }
TY - JOUR AU - Alberto Ibort AU - David Martínez Torres TI - Approximately holomorphic geometry and estimated transversality on 2-calibrated manifolds JO - Comptes Rendus. Mathématique PY - 2004 SP - 709 EP - 712 VL - 338 IS - 9 PB - Elsevier DO - 10.1016/j.crma.2004.03.003 LA - en ID - CRMATH_2004__338_9_709_0 ER -
Alberto Ibort; David Martínez Torres. Approximately holomorphic geometry and estimated transversality on 2-calibrated manifolds. Comptes Rendus. Mathématique, Volume 338 (2004) no. 9, pp. 709-712. doi : 10.1016/j.crma.2004.03.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.03.003/
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