Contact Geometry
نویسنده
چکیده
2 Contact manifolds 4 2.1 Contact manifolds and their submanifolds . . . . . . . . . . . . . . 6 2.2 Gray stability and the Moser trick . . . . . . . . . . . . . . . . . . 13 2.3 Contact Hamiltonians . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Darboux’s theorem and neighbourhood theorems . . . . . . . . . . 17 2.4.1 Darboux’s theorem . . . . . . . . . . . . . . . . . . . . . . . 17 2.4.2 Isotropic submanifolds . . . . . . . . . . . . . . . . . . . . . 19 2.4.3 Contact submanifolds . . . . . . . . . . . . . . . . . . . . . 24 2.4.4 Hypersurfaces . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.4.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.5 Isotopy extension theorems . . . . . . . . . . . . . . . . . . . . . . 32 2.5.1 Isotropic submanifolds . . . . . . . . . . . . . . . . . . . . . 32 2.5.2 Contact submanifolds . . . . . . . . . . . . . . . . . . . . . 34 2.5.3 Surfaces in 3–manifolds . . . . . . . . . . . . . . . . . . . . 36 2.6 Approximation theorems . . . . . . . . . . . . . . . . . . . . . . . . 37 2.6.1 Legendrian knots . . . . . . . . . . . . . . . . . . . . . . . . 38 2.6.2 Transverse knots . . . . . . . . . . . . . . . . . . . . . . . . 42
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