scholarly journals Deformations of coisotropic submanifolds in locally conformal symplectic manifolds

2016 ◽  
Vol 20 (3) ◽  
pp. 553-596 ◽  
Author(s):  
Hông Vân Lê ◽  
Yong-Geun Oh
Keyword(s):  
Symplectic Manifolds ◽  
Coisotropic Submanifolds ◽  
Locally Conformal

scholarly journals Topological and Dynamical Aspects of Jacobi Sigma Models

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1205
Author(s):  
Francesco Bascone ◽  
Franco Pezzella ◽  
Patrizia Vitale
Keyword(s):  
Sigma Models ◽  
Finite Dimension ◽  
Symplectic Manifolds ◽  
Target Space ◽  
Contact Manifolds ◽  
Gauge Symmetries ◽  
Jacobi Manifolds ◽  
Topological Field ◽  
Jacobi Manifold ◽  
Locally Conformal

The geometric properties of sigma models with target space a Jacobi manifold are investigated. In their basic formulation, these are topological field theories—recently introduced by the authors—which share and generalise relevant features of Poisson sigma models, such as gauge invariance under diffeomorphisms and finite dimension of the reduced phase space. After reviewing the main novelties and peculiarities of these models, we perform a detailed analysis of constraints and ensuing gauge symmetries in the Hamiltonian approach. Contact manifolds as well as locally conformal symplectic manifolds are discussed, as main instances of Jacobi manifolds.

ON LIE–RINEHART–JACOBI ALGEBRAS

2008 ◽  
Vol 07 (06) ◽  
pp. 749-772 ◽  
Author(s):  
EUGÈNE OKASSA
Keyword(s):  
Symplectic Manifolds ◽  
Lie Algebroids ◽  
Contact Manifolds ◽  
Poisson Algebras ◽  
Locally Conformal

We show that Jacobi algebras (Poisson algebras respectively) can be defined only as Lie–Rinehart–Jacobi algebras (as Lie–Rinehart–Poisson algebras respectively). Also we show that contact manifolds, locally conformal symplectic manifolds (symplectic manifolds respectively) can be defined only as symplectic Lie–Rinehart–Jacobi algebras (only as symplectic Lie–Rinehart–Poisson algebras respectively). We define symplectic Lie algebroids.

scholarly journals On locally conformal symplectic manifolds of the first kind

2018 ◽  
Vol 143 ◽  
pp. 1-57 ◽  
Author(s):  
Giovanni Bazzoni ◽  
Juan Carlos Marrero
Keyword(s):  
Symplectic Manifolds ◽  
Locally Conformal

scholarly journals Cohomology theories on locally conformal symplectic manifolds

2015 ◽  
Vol 19 (1) ◽  
pp. 45-82 ◽  
Author(s):  
Hông Vân Lê ◽  
Jiri Vanžura
Keyword(s):  
Symplectic Manifolds ◽  
Locally Conformal

scholarly journals Coisotropic Submanifolds in b-symplectic Geometry

2020 ◽  
pp. 1-32
Author(s):  
Stephane Geudens ◽  
Marco Zambon
Keyword(s):  
Normal Form ◽  
Symplectic Geometry ◽  
Symplectic Structure ◽  
Symplectic Manifolds ◽  
Coisotropic Submanifolds ◽  
Form Theorem ◽  
Degeneracy Locus ◽  
Normal Form Theorem

Abstract We study coisotropic submanifolds of b-symplectic manifolds. We prove that b-coisotropic submanifolds (those transverse to the degeneracy locus) determine the b-symplectic structure in a neighborhood, and provide a normal form theorem. This extends Gotay’s theorem in symplectic geometry. Further, we introduce strong b-coisotropic submanifolds and show that their coisotropic quotient, which locally is always smooth, inherits a reduced b-symplectic structure.

scholarly journals Locally conformal symplectic nilmanifolds with no locally conformal Kähler metrics

2017 ◽  
Vol 4 (1) ◽  
pp. 172-178
Author(s):  
Giovanni Bazzoni ◽  
Juan Carlos Marrero
Keyword(s):  
Symplectic Manifolds ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Locally Conformal Kähler ◽  
Locally Conformal

Abstract We report on a question, posed by L. Ornea and M. Verbitsky in [32], about examples of compact locally conformal symplectic manifolds without locally conformal Kähler metrics. We construct such an example on a compact 4-dimensional nilmanifold, not the product of a compact 3-manifold and a circle.

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