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تسجيل مستخدم جديدRegular Jacobi Structures and Generalized Contact Bundles
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تأليف
Jonas Schnitzer
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A Jacobi structure $J$ on a line bundle $Lto M$ is weakly regular if the sharp map $J^sharp : J^1 L to DL$ has constant rank. A generalized contact bundle with regular Jacobi structure possess a transverse complex structure. Paralleling the work of Bailey in generalized complex geometry, we find condition on a pair consisting of a regular Jacobi structure and an transverse complex structure to come from a generalized contact structure. In this way we are able to construct interesting examples of generalized contact bundles. As applications: 1) we prove that every 5-dimensional nilmanifold is equipped with an invariant generalized contact structure, 2) we show that, unlike the generalized complex case, all contact bundles over a complex manifold possess a compatible generalized contact structure. Finally we provide a counterexample presenting a locally conformal symplectic bundle over a generalized contact manifold of complex type that do not possess a compatible generalized contact structure.
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اقرأ أيضاً
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