2014/06/30 by Maria Amelia Salazar, IMPA, Brazil, María Amelia Salazar +1 · 7 citations
Mathematics · Medicine · Physics and Astronomy · #Algebra over a field #Dimension (graph theory) #Geometric Analysis and Curvature Flows #Geometry #Homotopy and Cohomology in Algebraic Topology #Isotropy #Mathematical analysis #Mathematical proof #Mathematics #Ophthalmology and Eye Disorders #Physics #Poisson distribution #Pure mathematics #Quantum mechanics #Symplectic geometry #math.DG #math.SG #nlin.SI
paper · pdf · doi:10.3842/sigma.2017.033
published in Symmetry Integrability and Geometry Methods and Applications (National Academy of Sciences of Ukraine)
openalex publication_date 2017/05/24 · arxiv created 2017/05/25 · arxiv updated 2017/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.