2012/08/28 by Hông Vân Lê, Yong-Geun Oh · 1 citation
Mathematics · #math.SG #math.DG #math.QA #msc:53D35
published as ASIAN J. MATH. Vol. 20, No. 3, pp. 555-598, July 2016 · 41 pages, some simplification and improvement in presentation, typos corrected. arXiv admin note: substantial text overlap with arXiv:math/0305292
arxiv created 2012/08/28 · arxiv updated 2016/06/21
In this paper, we study deformations of coisotropic submanifolds in a locally conformal symplectic manifold. Firstly, we derive the equation that governs C^∞ deformations of coisotropic submanifolds and define the corresponding C^∞-moduli space of coisotropic submanifolds modulo the Hamiltonian isotopies. Secondly, we prove that the formal deformation problem is governed by an L_∞-structure which is a \frak b-deformation of strong homotopy Lie algebroids introduced in Oh and Park (2005) in the symplectic context. Then we study deformations of locally conformal symplectic structures and their moduli space, and the corresponding bulk deformations of coisotropic submanifolds. Finally we revisit Zambon's obstructed infinitesimal deformation (Zambon, 2002) in this enlarged context and prove that it is still obstructed.