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Journal articles on the topic 'Locally conformal symplectic structures'

Author: Grafiati

Published: 17 September 2021

Last updated: 30 July 2025

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1

Bazzoni, Giovanni, and Alberto Raffero. "Special Types of Locally Conformal Closed G2-Structures." Axioms 7, no. 4 (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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2

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

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3

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 (2003): 151–58. http://dx.doi.org/10.1016/s0393-0440(02)00128-6.

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4

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 (2011): 311–37. http://dx.doi.org/10.1007/s10455-011-9259-z.

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5

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

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6

Origlia, Marcos. "Locally conformal symplectic structures on Lie algebras of type I and their solvmanifolds." Forum Mathematicum 31, no. 3 (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 produ

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7

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

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8

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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9

Alekseevsky, D. V., V. Cortés, K. Hasegawa, and Y. Kamishima. "Homogeneous locally conformally Kähler and Sasaki manifolds." International Journal of Mathematics 26, no. 06 (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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10

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

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11

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

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12

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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13

Bazzoni, Giovanni, and Juan Carlos Marrero. "Locally conformal symplectic nilmanifolds with no locally conformal Kähler metrics." Complex Manifolds 4, no. 1 (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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14

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

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15

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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16

OKASSA, EUGÈNE. "ON LIE–RINEHART–JACOBI ALGEBRAS." Journal of Algebra and Its Applications 07, no. 06 (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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17

Zając, Marcin, Cristina Sardón, and Orlando Ragnisco. "Time-Dependent Hamiltonian Mechanics on a Locally Conformal Symplectic Manifold." Symmetry 15, no. 4 (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 propert

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18

Liu, Jiefeng, Sihan Zhou, and Lamei Yuan. "Conformal r-matrix-Nijenhuis structures, symplectic-Nijenhuis structures, and ON-structures." Journal of Mathematical Physics 63, no. 10 (2022): 101701. http://dx.doi.org/10.1063/5.0101471.

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In this paper, we first study infinitesimal deformations of a Lie conformal algebra and a Lie conformal algebra with a module (called an [Formula: see text] pair), which lead to the notions of the Nijenhuis operator on the Lie conformal algebra and the Nijenhuis structure on the [Formula: see text] pair, respectively. Then, by adding compatibility conditions between Nijenhuis structures and [Formula: see text]-operators, we introduce the notion of an [Formula: see text]-structure on an [Formula: see text] pair and show that an [Formula: see text]-structure gives rise to a hierarchy of pairwise

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19

Bertelson, Mélanie, and Gaël Meigniez. "Conformal symplectic, foliated and contact structures." Journal of Symplectic Geometry 22, no. 2 (2024): 393–439. http://dx.doi.org/10.4310/jsg.240921013606.

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20

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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21

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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22

Gompf, Robert E. "Locally holomorphic maps yield symplectic structures." Communications in Analysis and Geometry 13, no. 3 (2005): 511–25. http://dx.doi.org/10.4310/cag.2005.v13.n3.a2.

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23

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

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24

NODA, TOMONORI. "SYMPLECTIC STRUCTURES ON STATISTICAL MANIFOLDS." Journal of the Australian Mathematical Society 90, no. 3 (2011): 371–84. http://dx.doi.org/10.1017/s1446788711001285.

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AbstractA relationship between symplectic geometry and information geometry is studied. The square of a dually flat space admits a natural symplectic structure that is the pullback of the canonical symplectic structure on the cotangent bundle of the dually flat space via the canonical divergence. With respect to the symplectic structure, there exists a moment map whose image is the dually flat space. As an example, we obtain a duality relation between the Fubini–Study metric on a projective space and the Fisher metric on a statistical model on a finite set. Conversely, a dually flat space admi

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25

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

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26

Ornea, Liviu, and Paolo Piccinni. "Locally conformal Kähler structures in quaternionic geometry." Transactions of the American Mathematical Society 349, no. 2 (1997): 641–55. http://dx.doi.org/10.1090/s0002-9947-97-01591-2.

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27

Wade, A�ssa. "Locally Conformal Dirac Structures and Infinitesimal Automorphisms." Communications in Mathematical Physics 246, no. 2 (2004): 295–310. http://dx.doi.org/10.1007/s00220-004-1047-1.

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28

Aikou, Tadashi. "Locally conformal Berwald spaces and Weyl structures." Publicationes Mathematicae Debrecen 49, no. 1-2 (1996): 113–26. http://dx.doi.org/10.5486/pmd.1996.1709.

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29

Yusuf, G. Y. "Geometry of Locally Conformal C-12 Manifolds." BASRA JOURNAL OF SCIENCE 41, no. 1 (2023): 13–30. http://dx.doi.org/10.29072/basjs.20230102.

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This study deals with the class of locally conformal manifolds in such a way that the characterization identity for the aforementioned class is produced. Furthermore, the first clan of Cartan's structure equations is determined when the components of Kirichenko's tensors on associated G-structures for locally conformal manifolds are determined. The second clan of Cartan's structural equations for locally conformal manifolds was also completed.

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30

Fernández, Marisa, Victor Manero, and Jonatan Sánchez. "The Laplacian Flow of Locally Conformal Calibrated G2-Structures." Axioms 8, no. 1 (2019): 7. http://dx.doi.org/10.3390/axioms8010007.

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We consider the Laplacian flow of locally conformal calibrated G 2 -structures as a natural extension to these structures of the well-known Laplacian flow of calibrated G 2 -structures. We study the Laplacian flow for two explicit examples of locally conformal calibrated G 2 manifolds and, in both cases, we obtain a flow of locally conformal calibrated G 2 -structures, which are ancient solutions, that is they are defined on a time interval of the form ( − ∞ , T ) , where T > 0 is a real number. Moreover, for each of these examples, we prove that the underlying metrics g ( t ) of the soluti

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31

SPENCER, JOSEPH A., and JAMES T. WHEELER. "THE EXISTENCE OF TIME." International Journal of Geometric Methods in Modern Physics 08, no. 02 (2011): 273–301. http://dx.doi.org/10.1142/s0219887811005130.

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Of those gauge theories of gravity known to be equivalent to general relativity, only the biconformal gauging introduces new structures — the quotient of the conformal group of any pseudo-Euclidean space by its Weyl subgroup always has natural symplectic and metric structures. Using this metric and symplectic form, we show that there exist canonically conjugate, orthogonal, metric submanifolds if and only if the original gauged space is Euclidean or signature 0. In the Euclidean cases, the resultant configuration space must be Lorentzian. Therefore, in this context, time may be viewed as a der

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32

Rao, R. Ranga. "Symplectic structures on locally compact abelian groups and polarizations." Proceedings Mathematical Sciences 104, no. 1 (1994): 217–23. http://dx.doi.org/10.1007/bf02830885.

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33

Shahid, M. Hasan, and Kouei Sekigawa. "Generic submanifolds of a locally conformal Kaehler manifold-II." International Journal of Mathematics and Mathematical Sciences 16, no. 3 (1993): 557–64. http://dx.doi.org/10.1155/s0161171293000687.

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The purpose of this paper is to study generic submanifolds with parallel structures, generic product submanifolds and totally umbilical submanifolds of a locally conformal Kaehler manifold. Moreover, we give some examples of generic submanifolds of a locally conformal Kaehler manifold which are notCR-submanifolds.

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34

Goto, Ryushi. "On the stability of locally conformal Kähler structures." Journal of the Mathematical Society of Japan 66, no. 4 (2014): 1375–401. http://dx.doi.org/10.2969/jmsj/06641375.

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35

Fino, Anna, and Alberto Raffero. "Einstein locally conformal calibrated $$G_2$$ G 2 -structures." Mathematische Zeitschrift 280, no. 3-4 (2015): 1093–106. http://dx.doi.org/10.1007/s00209-015-1468-x.

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36

Khuzwayo, Ntokozo Sibonelo, and Fortuné Massamba. "Some Properties of Curvature Tensors and Foliations of Locally Conformal Almost Kähler Manifolds." International Journal of Mathematics and Mathematical Sciences 2021 (February 17, 2021): 1–7. http://dx.doi.org/10.1155/2021/6673918.

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We investigate a class of locally conformal almost Kähler structures and prove that, under some conditions, this class is a subclass of almost Kähler structures. We show that a locally conformal almost Kähler manifold admits a canonical foliation whose leaves are hypersurfaces with the mean curvature vector field proportional to the Lee vector field. The geodesibility of the leaves is also characterized, and their minimality coincides with the incompressibility of the Lee vector field along the leaves.

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37

Hosseinzadeh, Vahid, and Kourosh Nozari. "Covariant statistical mechanics of non-Hamiltonian systems." International Journal of Geometric Methods in Modern Physics 15, no. 02 (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 s

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38

Mykytyuk, Ihor. "Reductions of Invariant bi-Poisson Structures and Locally Free Actions." Symmetry 13, no. 11 (2021): 2043. http://dx.doi.org/10.3390/sym13112043.

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Let (X,G,ω1,ω2,{ηt}) be a manifold with a bi-Poisson structure {ηt} generated by a pair of G-invariant symplectic structures ω1 and ω2, where a Lie group G acts properly on X. We prove that there exists two canonically defined manifolds (RLi,Gi,ω1i,ω2i,{ηit}), i=1,2 such that (1) RLi is a submanifold of an open dense subset X(H)⊂X; (2) symplectic structures ω1i and ω2i, generating a bi-Poisson structure {ηit}, are Gi- invariant and coincide with restrictions ω1|RLi and ω2|RLi; (3) the canonically defined group Gi acts properly and locally freely on RLi; (4) orbit spaces X(H)/G and RLi/Gi are c

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39

Bascone, Francesco, Franco Pezzella, and Patrizia Vitale. "Topological and Dynamical Aspects of Jacobi Sigma Models." Symmetry 13, no. 7 (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 manifol

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40

TORRES DEL CASTILLO, G. F., and E. GALINDO-LINARES. "SYMPLECTIC STRUCTURES AND HAMILTONIAN FUNCTIONS CORRESPONDING TO A SYSTEM OF ODES." International Journal of Geometric Methods in Modern Physics 10, no. 01 (2012): 1220023. http://dx.doi.org/10.1142/s021988781220023x.

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It is shown that, given a system of 2n first-order (or of n second-order) ODEs, there exists an infinite number of symplectic structures and Hamiltonian functions such that the corresponding Hamilton equations are locally equivalent to the given system of equations, without restrictions analogous to the Helmholtz conditions.

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41

Sawai, Hiroshi. "Locally conformal Kähler structures on compact nilmanifolds with left-invariant complex structures." Geometriae Dedicata 125, no. 1 (2007): 93–101. http://dx.doi.org/10.1007/s10711-007-9140-1.

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42

Mayrand, Maxence. "Stratification of singular hyperkähler quotients." Complex Manifolds 9, no. 1 (2022): 261–84. http://dx.doi.org/10.1515/coma-2021-0140.

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Abstract Hyperkähler quotients by non-free actions are typically singular, but are nevertheless partitioned into smooth hyperkähler manifolds. We show that these partitions are topological stratifications, in a strong sense. We also endow the quotients with global Poisson structures which recover the hyperkähler structures on the strata. Finally, we give a local model which shows that these quotients are locally isomorphic to linear complex-symplectic reductions in the GIT sense. These results can be thought of as the hyperkähler analogues of Sjamaar–Lerman’s theorems for singular symplectic r

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43

Bursztyn, Henrique, Hudson Lima, and Eckhard Meinrenken. "Splitting theorems for Poisson and related structures." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 754 (2019): 281–312. http://dx.doi.org/10.1515/crelle-2017-0014.

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Abstract According to the Weinstein splitting theorem, any Poisson manifold is locally, near any given point, a product of a symplectic manifold with another Poisson manifold whose Poisson structure vanishes at the point. Similar splitting results are known, e.g., for Lie algebroids, Dirac structures and generalized complex structures. In this paper, we develop a novel approach towards these results that leads to various generalizations, including their equivariant versions as well as their formulations in new contexts.

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44

Dragomir, Sorin. "Generalized Hopf manifolds, locally conformal Kaehler structures and real hypersurfaces." Kodai Mathematical Journal 14, no. 3 (1991): 366–91. http://dx.doi.org/10.2996/kmj/1138039462.

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45

shahid, M. Hasan, and A. Sharfuddin. "On Generic submanifolds of a locally conformal Kahler manifold with parallel canonical structures." International Journal of Mathematics and Mathematical Sciences 18, no. 2 (1995): 331–40. http://dx.doi.org/10.1155/s0161171295000421.

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The study ofCR-submanifolds of a Kähler manifold was initiated by Bejancu [1]. Since then many papers have appeared onCR-submanifolds of a Kähler manifold. Also, it has been studied that generic submanifolds of Kähler manifolds [2] are generalisations of holomorphic submanifolds, totally real submanifolds andCR-submanifolds of Kähler manifolds. On the other hand, many examplesC2of generic surfaces in which are notCR-submanifolds have been given by Chen [3] and this leads to the present paper where we obtain some necessary conditions for a generic submanifolds in a locally conformal Kähler mani

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46

Andrada, A., and M. Origlia. "Locally conformally Kähler solvmanifolds: a survey." Complex Manifolds 6, no. 1 (2019): 65–87. http://dx.doi.org/10.1515/coma-2019-0003.

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AbstractA Hermitian structure on a manifold is called locally conformally Kähler (LCK) if it locally admits a conformal change which is Kähler. In this survey we review recent results of invariant LCK structures on solvmanifolds and present original results regarding the canonical bundle of solvmanifolds equipped with a Vaisman structure, that is, a LCK structure whose associated Lee form is parallel.

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47

Oh, Seo-Hyeon, Jong-Wook Ha, and Keun Park. "Adaptive Conformal Cooling of Injection Molds Using Additively Manufactured TPMS Structures." Polymers 14, no. 1 (2022): 181. http://dx.doi.org/10.3390/polym14010181.

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In injection molding, cooling channels are usually manufactured with a straight shape, and thus have low cooling efficiency for a curved mold. Recently, additive manufacturing (AM) was used to fabricate conformal cooling channels that could maintain a consistent distance from the curved surface of the mold. Because this conformal cooling channel was designed to obtain a uniform temperature on the mold surface, it could not efficiently cool locally heated regions (hot spots). This study developed an adaptive conformal cooling method that supports localized-yet-uniform cooling for the heated reg

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48

Bridges, Thomas J. "Canonical multi-symplectic structure on the total exterior algebra bundle." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2069 (2006): 1531–51. http://dx.doi.org/10.1098/rspa.2005.1629.

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The aim of this paper is to construct multi-symplectic structures starting with the geometry of an oriented Riemannian manifold, independent of a Lagrangian or a particular partial differential equation (PDE). The principal observation is that on an n -dimensional orientable manifold M there is a canonical quadratic form Θ associated with the total exterior algebra bundle on M . On the fibre, which has dimension 2 n , the form Θ can be locally decomposed into n classical symplectic structures. When concatenated, these n -symplectic structures define a partial differential operator, J ∂ , which

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49

Fang, Hongyuan, Jianwei Lei, Man Yang, and Ziwei Li. "Analysis of GPR Wave Propagation Using CUDA-Implemented Conformal Symplectic Partitioned Runge-Kutta Method." Complexity 2019 (June 23, 2019): 1–14. http://dx.doi.org/10.1155/2019/4025878.

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Accurate forward modeling is of great significance for improving the accuracy and speed of inversion. For forward modeling of large sizes and fine structures, numerical accuracy and computational efficiency are not high, due to the stability conditions and the dense grid number. In this paper, the symplectic partitioned Runge-Kutta (SPRK) method, surface conformal technique, and graphics processor unit (GPU) acceleration technique are combined to establish a precise and efficient numerical model of electromagnetic wave propagation in complex geoelectric structures, with the goal of realizing a

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50

Yang, Man, Hongyuan Fang, Dazhong Chen, Xueming Du, and Fuming Wang. "The Conformal Finite-Difference Time-Domain Simulation of GPR Wave Propagation in Complex Geoelectric Structures." Geofluids 2020 (February 24, 2020): 1–14. http://dx.doi.org/10.1155/2020/3069372.

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The finite-difference time-domain (FDTD) method adopts the most popular numerical model simulating ground penetrating radar (GPR) wave propagation in an underground structure. However, a staircase approximation method is usually adopted to simulate the curved boundary of an irregular object in the FDTD and symplectic partitioned Runge-Kutta (SPRK) methods. The approximate processing of rectangular mesh parameters will result in calculation errors and virtual surface waves for irregular targets of an underground structure. In this paper, we examine transverse mode (TM) electromagnetic waves wit

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