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Academic literature on the topic 'Coisotropic submanifolds'

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Published: 10 March 2023

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Journal articles on the topic "Coisotropic submanifolds"

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VAISMAN, IZU. "TANGENT DIRAC STRUCTURES AND SUBMANIFOLDS." International Journal of Geometric Methods in Modern Physics 02, no. 05 (October 2005): 759–75. http://dx.doi.org/10.1142/s0219887805000843.

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We write down the local equations that characterize the submanifolds N of a Dirac manifold M which have a normal bundle that is either a coisotropic or an isotropic submanifold of TM endowed with the tangent Dirac structure. In the Poisson case, these formulas once again prove a result of Xu: the submanifold N has a normal bundle which is a coisotropic submanifold of TM with the tangent Poisson structure if and only if N is a Dirac submanifold. In the presymplectic case it is the isotropy of the normal bundle which characterizes the corresponding notion of a Dirac submanifold. On the way, we give a simple definition of the tangent Dirac structure, make new remarks about it and establish its characteristic, local formulas for various interesting classes of submanifolds of a Dirac manifold.
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Ali, Md Showkat, MG M. Talukder, and MR Khan. "Tangent Dirac Structures and Poisson Dirac Submanifolds." Dhaka University Journal of Science 62, no. 1 (February 7, 2015): 21–24. http://dx.doi.org/10.3329/dujs.v62i1.21955.

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The local equations that characterize the submanifolds N of a Dirac manifold M is an isotropic (coisotropic) submanifold of TM endowed with the tangent Dirac structure. In the Poisson case which is a result of Xu: the submanifold N has a normal bundle which is a coisotropic submanifold of TM with the tangent Poisson structure if and only if N is a Dirac submanifold. In this paper we have proved a theorem in the general Poisson case that the fixed point set MG has a natural induced Poisson structure that implies a Poisson-Dirac submanifolds, where G×M?M be a proper Poisson action. DOI: http://dx.doi.org/10.3329/dujs.v62i1.21955 Dhaka Univ. J. Sci. 62(1): 21-24, 2014 (January)
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GÜREL, BAŞAK Z. "TOTALLY NON-COISOTROPIC DISPLACEMENT AND ITS APPLICATIONS TO HAMILTONIAN DYNAMICS." Communications in Contemporary Mathematics 10, no. 06 (December 2008): 1103–28. http://dx.doi.org/10.1142/s0219199708003198.

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In this paper, we prove the Conley conjecture and the almost existence theorem in a neighborhood of a closed nowhere coisotropic submanifold under certain natural assumptions on the ambient symplectic manifold. Essential to the proofs is a displacement principle for such submanifolds. Namely, we show that a topologically displaceable nowhere coisotropic submanifold is also displaceable by a Hamiltonian diffeomorphism, partially extending the well-known non-Lagrangian displacement property.
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Zambon, Marco. "An example of coisotropic submanifolds C1-close to a given coisotropic submanifold." Differential Geometry and its Applications 26, no. 6 (December 2008): 635–37. http://dx.doi.org/10.1016/j.difgeo.2008.04.011.

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Schätz, Florian, and Marco Zambon. "Equivalences of coisotropic submanifolds." Journal of Symplectic Geometry 15, no. 1 (2017): 107–49. http://dx.doi.org/10.4310/jsg.2017.v15.n1.a4.

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Cattaneo, Alberto S. "Coisotropic Submanifolds and Dual Pairs." Letters in Mathematical Physics 104, no. 3 (October 26, 2013): 243–70. http://dx.doi.org/10.1007/s11005-013-0661-2.

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Ueki, Satoshi. "Leaf-wise intersections in coisotropic submanifolds." Kodai Mathematical Journal 36, no. 1 (March 2013): 91–98. http://dx.doi.org/10.2996/kmj/1364562721.

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Usher, Michael. "Local rigidity, symplectic homeomorphisms, and coisotropic submanifolds." Bulletin of the London Mathematical Society 54, no. 1 (February 2022): 45–53. http://dx.doi.org/10.1112/blms.12555.

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Lê, Hong Vân, Yong-Geun Oh, Alfonso G. Tortorella, and Luca Vitagliano. "Deformations of coisotropic submanifolds in Jacobi manifolds." Journal of Symplectic Geometry 16, no. 4 (2018): 1051–116. http://dx.doi.org/10.4310/jsg.2018.v16.n4.a7.

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Ginzburg, Viktor. "On Maslov class rigidity for coisotropic submanifolds." Pacific Journal of Mathematics 250, no. 1 (March 1, 2011): 139–61. http://dx.doi.org/10.2140/pjm.2011.250.139.

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Dissertations / Theses on the topic "Coisotropic submanifolds"

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Schätz, Florian. "Coisotropic submanifolds and the BFV-complex /." [S.l.] : [s.n.], 2009. http://opac.nebis.ch/cgi-bin/showAbstract.pl?sys=000286578.

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Sodoge, Tobias. "The geometry and topology of stable coisotropic submanifolds." Thesis, University College London (University of London), 2017. http://discovery.ucl.ac.uk/1570398/.

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In this thesis I study the geometry and topology of coisotropic submanifolds of sym- plectic manifolds. In particular of stable and of fibred coisotropic submanifolds. I prove that the symplectic quotient B of a stable, fibred coisotropic submanifold C is geometrically uniruled if one imposes natural geometric assumptions on C. The proof has four main steps. I first assign a Lagrangian graph LC and a stable hyper- surface HC to C, which both capture aspects of the geometry and topology of C. Second, I adapt and apply Floer theoretic methods to LC to establish existence of holomorphic discs with boundary on LC . I then stretch the neck around HC and ap- ply techniques from symplectic field theory to obtain more information about these holomorphic discs. Finally, I derive that this implies existence of a non-constant holomorphic sphere through any given point in B by glueing a holomorphic to an antiholomorphic disc along their common boundary and a simple argument.
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TORTORELLA, ALFONSO GIUSEPPE. "Deformations of coisotropic submanifolds in Jacobi manifolds." Doctoral thesis, 2017. http://hdl.handle.net/2158/1077777.

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In this thesis, we investigate deformation theory and moduli theory of coisotropic submanifolds in Jacobi manifolds. Originally introduced by Kirillov as local Lie algebras with one dimensional fibers, Jacobi manifolds encompass, unifying and generalizing, locally conformal symplectic manifolds, locally conformal Poisson manifolds, and non-necessarily coorientable contact manifolds. We attach an L-infinity-algebra to any coisotropic submanifold in a Jacobi manifold. Our construction generalizes and unifies analogous constructions by Oh-Park (symplectic case), Cattaneo-Felder (Poisson case), and Le-Oh (locally conformal symplectic case). As a completely new case we also associate an L-infinity-algebra with any coisotropic submanifold in a contact manifold. The L-infinity-algebra of a coisotropic submanifold S controls the formal coisotropic deformation problem of S, even under Hamiltonian equivalence, and provides criteria both for the obstructedness and for the unobstructedness at the formal level. Additionally we prove that if a certain condition ("fiberwise entireness") is satisfied then the L-infinity-algebra controls the non-formal coisotropic deformation problem, even under Hamiltonian equivalence. We associate a BFV-complex with any coisotropic submanifold in a Jacobi manifold. Our construction extends an analogous construction by Schatz in the Poisson setting, and in particular it also applies in the locally conformal symplectic/Poisson setting and the contact setting. Unlike the L-infinity-algebra, we prove that, with no need of any restrictive hypothesis, the BFV-complex of a coisotropic submanifold S controls the non-formal coisotropic deformation problem of S, even under both Hamiltonian equivalence and Jacobi equivalence. Notwithstanding the differences there is a close relation between the approaches to the coisotropic deformation problem via L-infinity-algebra and via BFV-complex. Indeed both the L-infinity-algebra and the BFV-complex of a coisotropic submanifold S provide a cohomological reduction of S. Moreover they are L-infinity quasi-isomorphic and so they encode equally well the moduli space of formal coisotropic deformations of S under Hamiltonian equivalence. In addition we exhibit two examples of coisotropic submanifolds in the contact setting whose coisotropic deformation problem is obstructed at the formal level. Further we provide a conceptual explanation of this phenomenon both in terms of the L-infinity-algebra and in terms of the BFV-complex.
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Conference papers on the topic "Coisotropic submanifolds"

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Aymerich-Valls, M., and J. C. Marrero. "Coisotropic submanifolds of linear Poisson manifolds and Lagrangian anchored vector subbundles of the symplectic cover." In XX INTERNATIONAL FALL WORKSHOP ON GEOMETRY AND PHYSICS. AIP, 2012. http://dx.doi.org/10.1063/1.4733372.

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