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On neighborhood theorems for symplectic pairs

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Abstract

Let M be a 2n-dimensional smooth manifold. We study local properties for a symplectic pair on M which is a pair of closed 2-forms of constant ranks with complementary kernel foliations. We show that some neighborhood theorems for submanifolds of M and Darboux type theorem hold. For more general case of recursion operators intertwining a pair of symplectic forms, we also prove that some neighborhood theorem holds.

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Authors and Affiliations

  1. School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, People’s Republic of China

    Hai-Long Her

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  1. Hai-Long Her
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Correspondence to Hai-Long Her.

Additional information

Partially supported by Project No. 10901084 and No. 11271269 of NSFC.

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Her, HL. On neighborhood theorems for symplectic pairs. J. Geom. 106, 163–174 (2015). https://doi.org/10.1007/s00022-014-0242-2

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  • DOI: https://doi.org/10.1007/s00022-014-0242-2

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