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Contact-pair neighborhood theorem for submanifolds in symplectic pairs |
Hai-Long HER() |
Department of Mathematics, Jinan University, Guangzhou 510632, China |
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Abstract Let M be a 2n-dimensional smooth manifold associated with the structure of symplectic pair which is a pair of closed 2-forms of constant ranks with complementary kernel foliations. Let Q⊂Mbe a codimension 2 compact submanifold. We show some sufficient and necessary conditions on the existence of the structure of contact pair (α,β) on Q,which is a pair of 1-forms of constant classes whose characteristic foliations are transverse and complementary such that α and β restrict to contact forms on the leaves of the characteristic foliations of βand α,respectively. This is a generalization of the neighborhood theorem for contact-type hypersurfaces in symplectic topology.
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Keywords
Symplectic pair
neighborhood theorem
contact pair
Liouville vector field
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Corresponding Author(s):
Hai-Long HER
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Issue Date: 23 September 2019
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