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SIGMA, 2017, Volume 13, 033, 44 pages (Mi sigma1233)  

This article is cited in 1 scientific paper (total in 1 paper)

Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators

María Amelia Salazara, Daniele Sepeb

a IMPA, Estrada Dona Castorina 110, Rio de Janeiro, Brazil 22460-320
b Universidade Federal Fluminense, Instituto de Matemática, Departamento de Matemática Aplicada, Rua Mário Santos Braga S/N, Campus do Valonguinho, Niterói, Brazil 24020-140

Abstract: Motivated by the importance of symplectic isotropic realisations in the study of Poisson manifolds, this paper investigates the local and global theory of contact isotropic realisations of Jacobi manifolds, which are those of minimal dimension. These arise naturally when considering multiplicity-free actions in contact geometry, as shown in this paper. The main results concern a classification of these realisations up to a suitable notion of isomorphism, as well as establishing a relation between the existence of symplectic and contact isotropic realisations for Poisson manifolds. The main tool is the classical Spencer operator which is related to Jacobi structures via their associated Lie algebroid, which allows to generalise previous results as well as providing more conceptual proofs for existing ones.

Keywords: Jacobi structures; contact manifolds; Poisson structures; projective structures; contact actions.

Funding Agency Grant Number
European Research Council 279729
Netherlands Organization for Scientific Research 639.031.345
M.A.S. would like to thank IMPA, CRM and MPIM Bonn for hospitality at various stages of the project. M.A.S. was partly supported by the DevMath programme of the Centre de Recerca Matemática and by the Max Planck Institute for Mathematics in Bonn. D.S. was partly supported by ERC starting grant 279729, by the NWO Veni grant 639.031.345 and by CNPq.


DOI: https://doi.org/10.3842/SIGMA.2017.033

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Full text: http://www.emis.de/.../033
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Bibliographic databases:

ArXiv: 1406.2138
MSC: 53D10; 53D17; 53D20; 37J15
Received: October 7, 2016; in final form May 17, 2017; Published online May 25, 2017
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Citation: María Amelia Salazar, Daniele Sepe, “Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators”, SIGMA, 13 (2017), 033, 44 pp.

Citation in format AMSBIB
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\by Mar{\'\i}a~Amelia~Salazar, Daniele~Sepe
\paper Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators
\jour SIGMA
\yr 2017
\vol 13
\papernumber 033
\totalpages 44
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\crossref{https://doi.org/10.3842/SIGMA.2017.033}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85019995313}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. Visinescu, “Sasaki-Ricci flow on Sasaki-Einstein space $T^{1,1}$ and deformations”, Int. J. Mod. Phys. A, 33:34, SI (2018), 1845014  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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