Reduction of Nambu-Poisson Manifolds by Regular Distributions

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Abstract

The version of Marsden-Ratiu reduction theorem for Nambu-Poisson manifolds by a regular distribution has been studied by Ibáñez et al. In this paper we show that the reduction is always ensured unless the distribution is zero. Next we extend the more general Falceto-Zambon Poisson reduction theorem for Nambu-Poisson manifolds. Finally, we define gauge transformations of Nambu-Poisson structures and show that these transformations commute with the reduction procedure.

Keywords

Reduction Nambu-Poisson manifolds Gauge transformations 

Mathematics Subject Classification (2010)

17B63 53C15 53D17 

Notes

Acknowledgments

The author wish to thank Prof. Goutam Mukherjee for his carefully reading the manuscript. The author would also like to thank the referee for his comments and suggestions on the earlier version of the paper that have improved the exposition.

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Stat-Math UnitIndian Statistical InstituteKolkataIndia

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