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Journal articles on the topic 'Coisotropic submanifolds'

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Published: 10 March 2023

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Kerman, Ely. "Displacement energy of coisotropic submanifolds and Hofer's geometry." Journal of Modern Dynamics 2, no. 3 (2008): 471–97. http://dx.doi.org/10.3934/jmd.2008.2.471.

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12

Ruan, Wei-Dong. "Deformation of integral coisotropic submanifolds in symplectic manifolds." Journal of Symplectic Geometry 3, no. 2 (2005): 161–69. http://dx.doi.org/10.4310/jsg.2005.v3.n2.a1.

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13

Tortorella, Alfonso Giuseppe. "Rigidity of integral coisotropic submanifolds of contact manifolds." Letters in Mathematical Physics 108, no. 3 (September 19, 2017): 883–96. http://dx.doi.org/10.1007/s11005-017-1005-4.

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14

Cattaneo, Alberto S., and Giovanni Felder. "Relative formality theorem and quantisation of coisotropic submanifolds." Advances in Mathematics 208, no. 2 (January 2007): 521–48. http://dx.doi.org/10.1016/j.aim.2006.03.010.

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15

Oh, Yong-Geun, and Jae-Suk Park. "Deformations of coisotropic submanifolds and strong homotopy Lie algebroids." Inventiones mathematicae 161, no. 2 (March 1, 2005): 287–360. http://dx.doi.org/10.1007/s00222-004-0426-8.

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16

Ziltener, Fabian. "Coisotropic submanifolds, leaf-wise fixed points, and presymplectic embeddings." Journal of Symplectic Geometry 8, no. 1 (2010): 95–118. http://dx.doi.org/10.4310/jsg.2010.v8.n1.a6.

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17

Vân Lê, Hông, and Yong-Geun Oh. "Deformations of coisotropic submanifolds in locally conformal symplectic manifolds." Asian Journal of Mathematics 20, no. 3 (2016): 553–96. http://dx.doi.org/10.4310/ajm.2016.v20.n3.a7.

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18

Schätz, Florian, and Marco Zambon. "Deformations of Coisotropic Submanifolds for Fibrewise Entire Poisson Structures." Letters in Mathematical Physics 103, no. 7 (February 15, 2013): 777–91. http://dx.doi.org/10.1007/s11005-013-0614-9.

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19

Kieserman, Noah. "The Liouville phenomenon in the deformation of coisotropic submanifolds." Differential Geometry and its Applications 28, no. 1 (February 2010): 121–30. http://dx.doi.org/10.1016/j.difgeo.2009.09.004.

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20

Müller, Stefan. "C0-characterization of symplectic and contact embeddings and Lagrangian rigidity." International Journal of Mathematics 30, no. 09 (August 2019): 1950035. http://dx.doi.org/10.1142/s0129167x19500356.

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We present a novel [Formula: see text]-characterization of symplectic embeddings and diffeomorphisms in terms of Lagrangian embeddings. Our approach is based on the shape invariant, which was discovered by Sikorav and Eliashberg, intersection theory and the displacement energy of Lagrangian submanifolds, and the fact that non-Lagrangian submanifolds can be displaced immediately. This characterization gives rise to a new proof of [Formula: see text]-rigidity of symplectic embeddings and diffeomorphisms. The various manifestations of Lagrangian rigidity that are used in our arguments come from [Formula: see text]-holomorphic curve methods. An advantage of our techniques is that they can be adapted to a [Formula: see text]-characterization of contact embeddings and diffeomorphisms in terms of coisotropic (or pre-Lagrangian) embeddings, which in turn leads to a proof of [Formula: see text]-rigidity of contact embeddings and diffeomorphisms. We give a detailed treatment of the shape invariants of symplectic and contact manifolds, and demonstrate that shape is often a natural language in symplectic and contact topology. We consider homeomorphisms that preserve shape, and propose a hierarchy of notions of Lagrangian topological submanifold. Moreover, we discuss shape-related necessary and sufficient conditions for symplectic and contact embeddings, and define a symplectic capacity from the shape.

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21

Ji, Xiang. "On equivalence of deforming Lie subalgebroids and deforming coisotropic submanifolds." Journal of Geometry and Physics 116 (June 2017): 258–70. http://dx.doi.org/10.1016/j.geomphys.2017.01.023.

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22

Frégier, Yaël, and Marco Zambon. "Simultaneous deformations and Poisson geometry." Compositio Mathematica 151, no. 9 (May 4, 2015): 1763–90. http://dx.doi.org/10.1112/s0010437x15007277.

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We consider the problem of deforming simultaneously a pair of given structures. We show that such deformations are governed by an $L_{\infty }$-algebra, which we construct explicitly. Our machinery is based on Voronov’s derived bracket construction. In this paper we consider only geometric applications, including deformations of coisotropic submanifolds in Poisson manifolds, of twisted Poisson structures, and of complex structures within generalized complex geometry. These applications cannot be, to our knowledge, obtained by other methods such as operad theory.

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23

Cattaneo>, Alberto S. "On the Integration of Poisson Manifolds, Lie Algebroids, and Coisotropic Submanifolds." Letters in Mathematical Physics 67, no. 1 (January 2004): 33–48. http://dx.doi.org/10.1023/b:math.0000027690.76935.f3.

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24

Cattaneo, Alberto S., and Giovanni Felder. "Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model." Letters in Mathematical Physics 69, no. 1-3 (July 2004): 157–75. http://dx.doi.org/10.1007/s11005-004-0609-7.

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25

Ziltener, Fabian. "On the Strict Arnold Chord Property and Coisotropic Submanifolds of Complex Projective Space." International Mathematics Research Notices 2016, no. 3 (June 4, 2015): 795–826. http://dx.doi.org/10.1093/imrn/rnv153.

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26

Usher, Michael. "Boundary depth in Floer theory and its applications to Hamiltonian dynamics and coisotropic submanifolds." Israel Journal of Mathematics 184, no. 1 (July 31, 2011): 1–57. http://dx.doi.org/10.1007/s11856-011-0058-9.

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27

SANDON, SHEILA. "ON ITERATED TRANSLATED POINTS FOR CONTACTOMORPHISMS OF ℝ2n+1 AND ℝ2n × S1." International Journal of Mathematics 23, no. 02 (February 2012): 1250042. http://dx.doi.org/10.1142/s0129167x12500425.

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A point q in a contact manifold is called a translated point for a contactomorphism ϕ with respect to some fixed contact form if ϕ(q) and q belong to the same Reeb orbit and the contact form is preserved at q. The problem of existence of translated points has an interpretation in terms of Reeb chords between Legendrian submanifolds, and can be seen as a special case of the problem of leafwise coisotropic intersections. For a compactly supported contactomorphism ϕ of ℝ2n+1 or ℝ2n × S1 contact isotopic to the identity, existence of translated points follows immediately from Chekanov's theorem on critical points of quasi-functions and Bhupal's graph construction. In this article we prove that if ϕ is positive then there are infinitely many nontrivial geometrically distinct iterated translated points, i.e. translated points of some iteration ϕk. This result can be seen as a (partial) contact analog of the result of Viterbo on existence of infinitely many iterated fixed points for compactly supported Hamiltonian symplectomorphisms of ℝ2n, and is obtained with generating functions techniques.

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28

KILIÇ, Erol, and Mehmet GÜLBAHAR. "Ideality of a Coisotropic Lightlike Submanifold." International Electronic Journal of Geometry 9, no. 1 (April 30, 2016): 89–99. http://dx.doi.org/10.36890/iejg.591898.

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29

Geudens, Stephane, and Marco Zambon. "Coisotropic Submanifolds in b-symplectic Geometry." Canadian Journal of Mathematics, February 24, 2020, 1–32. http://dx.doi.org/10.4153/s0008414x20000140.

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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.

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30

(ÖNEN) POYRAZ, NERGİZ, and BURÇİN DOĞAN. "GEOMETRY OF SEMI-INVARIANT COISOTROPIC SUBMANIFOLDS IN GOLDEN SEMI-RIEMANNIAN MANIFOLDS." Journal of Universal Mathematics, July 29, 2019, 113–21. http://dx.doi.org/10.33773/jum.537651.

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