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Journal articles on the topic 'Locally conformally symplectic'

Author: Grafiati

Published: 7 December 2024

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1

Belgun, F., O. Goertsches, and D. Petrecca. "Locally conformally symplectic convexity." Journal of Geometry and Physics 135 (January 2019): 235–52. http://dx.doi.org/10.1016/j.geomphys.2018.10.001.

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2

Otiman, Alexandra. "Locally conformally symplectic bundles." Journal of Symplectic Geometry 16, no. 5 (2018): 1377–408. http://dx.doi.org/10.4310/jsg.2018.v16.n5.a5.

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3

Stanciu, Miron. "Locally conformally symplectic reduction." Annals of Global Analysis and Geometry 56, no. 2 (June 3, 2019): 245–75. http://dx.doi.org/10.1007/s10455-019-09666-9.

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4

Bazzoni, Giovanni. "Locally conformally symplectic and Kähler geometry." EMS Surveys in Mathematical Sciences 5, no. 1 (November 19, 2018): 129–54. http://dx.doi.org/10.4171/emss/29.

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5

Gatsé, Servais Cyr. "AN EXAMPLE OF LOCALLY CONFORMALLY SYMPLECTIC MANIFOLDS." Advances in Mathematics: Scientific Journal 12, no. 1 (January 21, 2023): 187–92. http://dx.doi.org/10.37418/amsj.12.1.12.

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6

Bande, G., and D. Kotschick. "Moser stability for locally conformally symplectic structures." Proceedings of the American Mathematical Society 137, no. 07 (January 28, 2009): 2419–24. http://dx.doi.org/10.1090/s0002-9939-09-09821-9.

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7

Alekseevsky, D. V., V. Cortés, K. Hasegawa, and Y. Kamishima. "Homogeneous locally conformally Kähler and Sasaki manifolds." International Journal of Mathematics 26, no. 06 (June 2015): 1541001. http://dx.doi.org/10.1142/s0129167x15410013.

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We prove various classification results for homogeneous locally conformally symplectic manifolds. In particular, we show that a homogeneous locally conformally Kähler manifold of a reductive group is of Vaisman type if the normalizer of the isotropy group is compact. We also show that such a result does not hold in the case of non-compact normalizer and determine all left-invariant lcK structures on reductive Lie groups.

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8

Esen, Oğul, Manuel de León, Cristina Sardón, and Marcin Zajşc. "Hamilton–Jacobi formalism on locally conformally symplectic manifolds." Journal of Mathematical Physics 62, no. 3 (March 1, 2021): 033506. http://dx.doi.org/10.1063/5.0021790.

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9

Stanciu, Miron. "Locally conformally symplectic reduction of the cotangent bundle." Annals of Global Analysis and Geometry 61, no. 3 (January 16, 2022): 533–51. http://dx.doi.org/10.1007/s10455-021-09815-z.

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10

Otiman, Alexandra, and Miron Stanciu. "Darboux–Weinstein theorem for locally conformally symplectic manifolds." Journal of Geometry and Physics 111 (January 2017): 1–5. http://dx.doi.org/10.1016/j.geomphys.2016.10.006.

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11

Gatse, Servais Cyr. "Hamiltonian vector field on locally conformally symplectic manifold." International Mathematical Forum 11 (2016): 933–41. http://dx.doi.org/10.12988/imf.2016.6666.

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12

Angella, Daniele, Alexandra Otiman, and Nicoletta Tardini. "Cohomologies of locally conformally symplectic manifolds and solvmanifolds." Annals of Global Analysis and Geometry 53, no. 1 (July 17, 2017): 67–96. http://dx.doi.org/10.1007/s10455-017-9568-y.

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13

Angella, Daniele, Giovanni Bazzoni, and Maurizio Parton. "Structure of locally conformally symplectic Lie algebras and solvmanifolds." ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE 20, no. 2 (March 31, 2020): 373–411. http://dx.doi.org/10.2422/2036-2145.201708_015.

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14

Apostolov, Vestislav, and Georges Dloussky. "On the Lee classes of locally conformally symplectic complex surfaces." Journal of Symplectic Geometry 16, no. 4 (2018): 931–58. http://dx.doi.org/10.4310/jsg.2018.v16.n4.a2.

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15

Apostolov, Vestislav, and Georges Dloussky. "Locally Conformally Symplectic Structures on Compact Non-Kähler Complex Surfaces." International Mathematics Research Notices 2016, no. 9 (July 25, 2015): 2717–47. http://dx.doi.org/10.1093/imrn/rnv211.

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16

Chen, Youming, and Song Yang. "On the blow-up of points on locally conformally symplectic manifolds." Comptes Rendus Mathematique 354, no. 4 (April 2016): 411–14. http://dx.doi.org/10.1016/j.crma.2016.01.002.

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17

Vaisman, Izu. "Locally conformal symplectic manifolds." International Journal of Mathematics and Mathematical Sciences 8, no. 3 (1985): 521–36. http://dx.doi.org/10.1155/s0161171285000564.

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A locally conformal symplectic (l. c. s.) manifold is a pair(M2n,Ω)whereM2n(n>1)is a connected differentiable manifold, andΩa nondegenerate2-form onMsuch thatM=⋃αUα(Uα- open subsets).Ω/Uα=eσαΩα,σα:Uα→ℝ,dΩα=0. Equivalently,dΩ=ω∧Ωfor some closed1-formω. L. c. s. manifolds can be seen as generalized phase spaces of Hamiltonian dynamical systems since the form of the Hamilton equations is, in fact, preserved by homothetic canonical transformations. The paper discusses first Hamiltonian vector fields, and infinitesimal automorphisms (i. a.) on l. c. s. manifolds. If(M,Ω)has an i. a.Xsuch thatω(X)≠0, we say thatMis of the first kind andΩassumes the particular formΩ=dθ−ω∧θ. Such anMis a2-contact manifold with the structure forms(ω,θ), and it has a vertical2-dimensional foliationV. IfVis regular, we can give a fibration theorem which shows thatMis aT2-principal bundle over a symplectic manifold. Particularly,Vis regular for some homogeneous l. c. s, manifolds, and this leads to a general construction of compact homogeneous l. c. s, manifolds. Various related geometric results, including reductivity theorems for Lie algebras of i. a. are also given. Most of the proofs are adaptations of corresponding proofs in symplectic and contact geometry. The paper ends with an Appendix which states an analogous fibration theorem in Riemannian geometry.

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18

Bazzoni, Giovanni, and Juan Carlos Marrero. "Locally conformal symplectic nilmanifolds with no locally conformal Kähler metrics." Complex Manifolds 4, no. 1 (November 27, 2017): 172–78. http://dx.doi.org/10.1515/coma-2017-0011.

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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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19

Yang, Song, Xiangdong Yang, and Guosong Zhao. "Locally conformal symplectic blow-ups." Differential Geometry and its Applications 50 (February 2017): 11–19. http://dx.doi.org/10.1016/j.difgeo.2016.10.006.

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20

Bazzoni, Giovanni, and Alberto Raffero. "Special Types of Locally Conformal Closed G2-Structures." Axioms 7, no. 4 (November 28, 2018): 90. http://dx.doi.org/10.3390/axioms7040090.

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Motivated by known results in locally conformal symplectic geometry, we study different classes of G 2 -structures defined by a locally conformal closed 3-form. In particular, we provide a complete characterization of invariant exact locally conformal closed G 2 -structures on simply connected Lie groups, and we present examples of compact manifolds with different types of locally conformal closed G 2 -structures.

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21

OKASSA, EUGÈNE. "ON LIE–RINEHART–JACOBI ALGEBRAS." Journal of Algebra and Its Applications 07, no. 06 (December 2008): 749–72. http://dx.doi.org/10.1142/s0219498808003107.

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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.

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22

Zając, Marcin, Cristina Sardón, and Orlando Ragnisco. "Time-Dependent Hamiltonian Mechanics on a Locally Conformal Symplectic Manifold." Symmetry 15, no. 4 (April 1, 2023): 843. http://dx.doi.org/10.3390/sym15040843.

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In this paper we aim at presenting a concise but also comprehensive study of time-dependent (t-dependent) Hamiltonian dynamics on a locally conformal symplectic (lcs) manifold. We present a generalized geometric theory of canonical transformations in order to formulate an explicitly time-dependent geometric Hamilton-Jacobi theory on lcs manifolds, extending our previous work with no explicit time-dependence. In contrast to previous papers concerning locally conformal symplectic manifolds, the introduction of the time dependency that this paper presents, brings out interesting geometric properties, as it is the case of contact geometry in locally symplectic patches. To conclude, we show examples of the applications of our formalism, in particular, we present systems of differential equations with time-dependent parameters, which admit different physical interpretations as we shall point out.

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23

Haller, Stefan, and Tomasz Rybicki. "Reduction for locally conformal symplectic manifolds." Journal of Geometry and Physics 37, no. 3 (February 2001): 262–71. http://dx.doi.org/10.1016/s0393-0440(00)00050-4.

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24

Lê, Hông Vân, and Jiri Vanžura. "Cohomology theories on locally conformal symplectic manifolds." Asian Journal of Mathematics 19, no. 1 (2015): 45–82. http://dx.doi.org/10.4310/ajm.2015.v19.n1.a3.

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25

Banyaga, A. "Some properties of locally conformal symplectic structures." Commentarii Mathematici Helvetici 77, no. 2 (June 1, 2002): 383–98. http://dx.doi.org/10.1007/s00014-002-8345-z.

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26

Bazzoni, Giovanni, and Juan Carlos Marrero. "On locally conformal symplectic manifolds of the first kind." Bulletin des Sciences Mathématiques 143 (March 2018): 1–57. http://dx.doi.org/10.1016/j.bulsci.2017.10.001.

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27

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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28

Banyaga, Augustin. "Examples of non d ω-exact locally conformal symplectic forms." Journal of Geometry 87, no. 1-2 (November 2007): 1–13. http://dx.doi.org/10.1007/s00022-006-1849-8.

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29

Kadobianski, Roman, Jan Kubarski, Vitalij Kushnirevitch, and Robert Wolak. "Transitive Lie algebroids of rank 1 and locally conformal symplectic structures." Journal of Geometry and Physics 46, no. 2 (May 2003): 151–58. http://dx.doi.org/10.1016/s0393-0440(02)00128-6.

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30

Marrero, Juan C., David Martínez Torres, and Edith Padrón. "Universal models via embedding and reduction for locally conformal symplectic structures." Annals of Global Analysis and Geometry 40, no. 3 (March 8, 2011): 311–37. http://dx.doi.org/10.1007/s10455-011-9259-z.

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31

Hosseinzadeh, Vahid, and Kourosh Nozari. "Covariant statistical mechanics of non-Hamiltonian systems." International Journal of Geometric Methods in Modern Physics 15, no. 02 (January 24, 2018): 1850017. http://dx.doi.org/10.1142/s0219887818500172.

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In this paper, using the elegant language of differential forms, we provide a covariant formulation of the equilibrium statistical mechanics of non-Hamiltonian systems. The key idea of the paper is to focus on the structure of phase space and its kinematical and dynamical roles. While in the case of Hamiltonian systems, the structure of the phase space is a symplectic structure (a nondegenerate closed two-form), we consider an almost symplectic structure for the more general case of non-Hamiltonian systems. An almost symplectic structure is a nondegenerate but not necessarily closed two-form structure. Consequently, the dynamics becomes non-Hamiltonian and based on the fact that the structure is nondegenerate, we can also define a volume element. With a well-defined volume in hand, we derive the Liouville equation and find an invariant statistical state. Recasting non-Hamiltonian systems in terms of the almost symplectic geometry has at least two advantages: the formalism is covariant and therefore does not depend on coordinates and there is no confusion in the determination of the natural volume element of the system. For clarification, we investigate the application of the formalism in two examples in which the underlying geometry of the phase space is locally conformal symplectic geometry.

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32

Noda, Tomonori. "Reduction of locally conformal symplectic manifolds with examples of non-Kähler manifolds." Tsukuba Journal of Mathematics 28, no. 1 (June 2004): 127–36. http://dx.doi.org/10.21099/tkbjm/1496164717.

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33

Bascone, Francesco, Franco Pezzella, and Patrizia Vitale. "Topological and Dynamical Aspects of Jacobi Sigma Models." Symmetry 13, no. 7 (July 5, 2021): 1205. http://dx.doi.org/10.3390/sym13071205.

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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.

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34

Origlia, Marcos. "Locally conformal symplectic structures on Lie algebras of type I and their solvmanifolds." Forum Mathematicum 31, no. 3 (May 1, 2019): 563–78. http://dx.doi.org/10.1515/forum-2018-0200.

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Abstract We study Lie algebras of type I, that is, a Lie algebra {\mathfrak{g}} where all the eigenvalues of the operator {\operatorname{ad}_{X}} are imaginary for all {X\in\mathfrak{g}} . We prove that the Morse–Novikov cohomology of a Lie algebra of type I is trivial for any closed 1-form. We focus on locally conformal symplectic structures (LCS) on Lie algebras of type I. In particular, we show that for a Lie algebra of type I any LCS structure is of the first kind. We also exhibit lattices for some 6-dimensional Lie groups of type I admitting left invariant LCS structures in order to produce compact solvmanifolds equipped with an invariant LCS structure.

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35

Andrada, A., and M. Origlia. "Lattices in almost abelian Lie groups with locally conformal Kähler or symplectic structures." manuscripta mathematica 155, no. 3-4 (April 28, 2017): 389–417. http://dx.doi.org/10.1007/s00229-017-0938-3.

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36

Origlia, M. "On a certain class of locally conformal symplectic structures of the second kind." Differential Geometry and its Applications 68 (February 2020): 101586. http://dx.doi.org/10.1016/j.difgeo.2019.101586.

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37

Savelyev, Yasha. "Locally conformally symplectic deformation of Gromov non-squeezing." Archiv der Mathematik, October 9, 2023. http://dx.doi.org/10.1007/s00013-023-01922-6.

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38

Apostolov, Vestislav, and Georges Dloussky. "Twisted differentials and Lee classes of locally conformally symplectic complex surfaces." Mathematische Zeitschrift 303, no. 3 (February 23, 2023). http://dx.doi.org/10.1007/s00209-023-03242-5.

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39

Barbaro, Giuseppe, and Mehdi Lejmi. "Second Chern-Einstein metrics on four-dimensional almost-Hermitian manifolds." Complex Manifolds 10, no. 1 (January 1, 2023). http://dx.doi.org/10.1515/coma-2022-0150.

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Abstract We study four-dimensional second Chern-Einstein almost-Hermitian manifolds. In the compact case, we observe that under a certain hypothesis, the Riemannian dual of the Lee form is a Killing vector field. We use that observation to describe four-dimensional compact second Chern-Einstein locally conformally symplectic manifolds, and we give some examples of such manifolds. Finally, we study the second Chern-Einstein problem on unimodular almost-abelian Lie algebras, classifying those that admit a left-invariant second Chern-Einstein metric with a parallel non-zero Lee form.

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40

Oh, Yong-Geun, and Yasha Savelyev. "Pseudoholomorphic curves on the LCS-fication of contact manifolds." Advances in Geometry, June 3, 2023. http://dx.doi.org/10.1515/advgeom-2023-0004.

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Abstract For each contact diffeomorphism ϕ : (Q, ξ) → (Q, ξ) of (Q, ξ), we equip its mapping torus Mϕ with a locally conformal symplectic form of Banyaga’s type, which we call the lcs mapping torus of the contact diffeomorphism ϕ. In the present paper, we consider the product Q × S 1 = M id (corresponding to ϕ = id) and develop basic analysis of the associated J-holomorphic curve equation, which has the form ∂ ˉ π w = 0 , w ∗ λ ∘ j = f ∗ d θ $$ \bar{\partial}^{\pi} w=0, \quad w^{*} \lambda \circ j=f^{*} d \theta $$ for the map u = (w, f) : Σ ˙ → Q × S 1 $\dot{\Sigma} \rightarrow Q \times S^{1}$ for a λ-compatible almost complex structure J and a punctured Riemann surface ( Σ ˙ , j ) . $(\dot{\Sigma}, j).$ In particular, w is a contact instanton in the sense of [31], [32].We develop a scheme of treating the non-vanishing charge by introducing the notion of charge class in H 1 ( Σ ˙ , Z ) $H^{1}(\dot{\Sigma}, \mathbb{Z})$ and develop the geometric framework for the study of pseudoholomorphic curves, a correct choice of energy and the definition of moduli spaces towards the construction of a compactification of the moduli space on the lcs-fication of (Q, λ) (more generally on arbitrary locally conformal symplectic manifolds).

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41

Fiorucci, Adrien, and Romain Ruzziconi. "Charge algebra in Al(A)dSn spacetimes." Journal of High Energy Physics 2021, no. 5 (May 2021). http://dx.doi.org/10.1007/jhep05(2021)210.

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Abstract The gravitational charge algebra of generic asymptotically locally (A)dS spacetimes is derived in n dimensions. The analysis is performed in the Starobinsky/Fefferman-Graham gauge, without assuming any further boundary condition than the minimal falloffs for conformal compactification. In particular, the boundary structure is allowed to fluctuate and plays the role of source yielding some symplectic flux at the boundary. Using the holographic renormalization procedure, the divergences are removed from the symplectic structure, which leads to finite expressions. The charges associated with boundary diffeomorphisms are generically non-vanishing, non-integrable and not conserved, while those associated with boundary Weyl rescalings are non-vanishing only in odd dimensions due to the presence of Weyl anomalies in the dual theory. The charge algebra exhibits a field-dependent 2-cocycle in odd dimensions. When the general framework is restricted to three-dimensional asymptotically AdS spacetimes with Dirichlet boundary conditions, the 2-cocycle reduces to the Brown-Henneaux central extension. The analysis is also specified to leaky boundary conditions in asymptotically locally (A)dS spacetimes that lead to the Λ-BMS asymptotic symmetry group. In the flat limit, the latter contracts into the BMS group in n dimensions.

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42

Tchuiaga, Stéphane. "Towards the cosymplectic topology." Complex Manifolds 10, no. 1 (January 1, 2023). http://dx.doi.org/10.1515/coma-2022-0151.

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Abstract In this article, the cosymplectic analogue of the symplectic flux homomorphism of a compact connected cosymplectic manifold ( M , η , ω ) \left(M,\eta ,\omega ) with ∂ M = ∅ \partial M=\varnothing is studied. This is a continuous map with respect to the C 0 {C}^{0} -metric, whose kernel is connected by smooth arcs and coincides with the subgroup of all weakly Hamiltonian diffeomorphisms. We discuss the cosymplectic analogue of the Weinstein’s chart, and derive that the group G η , ω ( M ) {G}_{\eta ,\omega }\left(M) of all cosymplectic diffeomorphisms isotopic to the identity map is locally contractible. A study of an analogue of Polterovich’s regularization process for co-Hamiltonian isotopies follows. Finally, we study Moser’s stability theorems for locally conformal cosymplectic manifolds.

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43

Yau, Shing-Tung, Quanting Zhao, and Fangyang Zheng. "On Strominger Kähler-like manifolds with degenerate torsion." Transactions of the American Mathematical Society, February 28, 2023. http://dx.doi.org/10.1090/tran/8659.

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In this paper, we study a special type of compact Hermitian manifolds that are Strominger Kähler-like, or SKL for short. This condition means that the Strominger connection (also known as Bismut connection) is Kähler-like, in the sense that its curvature tensor obeys all the symmetries of the curvature of a Kähler manifold. Previously, we have shown that any SKL manifold ( M n , g ) (M^n,g) is always pluriclosed, and when the manifold is compact and g g is not Kähler, it cannot admit any balanced or strongly Gauduchon (in the sense of Popovici) metric. Also, when n = 2 n=2 , the SKL condition is equivalent to the Vaisman condition. In this paper, we give a classification for compact non-Kähler SKL manifolds in dimension 3 3 and those with degenerate torsion in higher dimensions. We also present some properties about SKL manifolds in general dimensions, for instance, given any compact non-Kähler SKL manifold, its Kähler form represents a non-trivial Aeppli cohomology class, the metric can never be locally conformal Kähler when n ≥ 3 n\geq 3 , and the manifold does not admit any Hermitian symplectic metric.

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