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Title: Generalized Kählerian manifolds and transformation of generalized contact structures (English)
Author: Bouzir, Habib
Author: Beldjilali, Gherici
Author: Belkhelfa, Mohamed
Author: Wade, Aissa
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 53
Issue: 1
Year: 2017
Pages: 35-48
Summary lang: English
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Category: math
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Summary: The aim of this paper is two-fold. First, new generalized Kähler manifolds are constructed starting from both classical almost contact metric and almost Kählerian manifolds. Second, the transformation construction on classical Riemannian manifolds is extended to the generalized geometry setting. (English)
Keyword: product manifolds
Keyword: trans-Sasakian manifolds
Keyword: generalized Kählerian manifolds
Keyword: generalized contact structures
Keyword: transformation of generalized almost contact structures
Keyword: generalized almost complex structures
MSC: 53C10
MSC: 53C15
MSC: 53C18
MSC: 53D25
idZBL: Zbl 06738497
idMR: MR3636680
DOI: 10.5817/AM2017-1-35
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Date available: 2017-03-23T10:05:45Z
Last updated: 2018-01-10
Stable URL: http://hdl.handle.net/10338.dmlcz/146074
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Reference: [1] Apostolov, V., Gualtieri, M.: Generalized Kähler manifolds, commuting complex structures, and split tangent bundles.Comm. Math. Phys. 2 (2007), 561–575. Zbl 1135.53018, MR 2287917, 10.1007/s00220-007-0196-4
Reference: [2] Beem, J.K., Ehrlich, P.E., Powell, Th.G.: Warped product manifolds in relativity.Selected studies: physics-astrophysics, mathematics, history of science, North-Holland, Amsterdam-New York, 1982, pp. 41–56. Zbl 0491.53047, MR 0662851
Reference: [3] Beldjilali, G., Belkhelfa, M.: Kählerian structures and $\mathcal{D}$-homothetic Bi-warping.J. Geom. Symmetry Phys. 42 (2016), 1–13. MR 3586441
Reference: [4] Blair, D.E.: Contact manifolds in Riemannian geometry.Lecture Notes in Mathematics, vol. 509, Springer, 1976, pp. 17–35. Zbl 0319.53026, MR 0467588
Reference: [5] Blair, D.E.: Riemannian geometry of contact and symplectic manifolds.Progress in Mathematics, vol. 203, Birkhäuser Boston, 2002. Zbl 1011.53001, MR 1874240
Reference: [6] Blair, D.E.: $\mathcal{D}$-homothetic warping.Publ. Inst. Math. (Beograd) (N.S.) 94 (108) (2013), 47–54. MR 3137489, 10.2298/PIM1308047B
Reference: [7] Blair, D.E., Oubiña, J.A.: Conformal and related changes of metric on the product of two almost contact metric manifolds.Publ. Mat. 34 (1) (1990), 199–207. Zbl 0721.53035, MR 1059874, 10.5565/PUBLMAT_34190_15
Reference: [8] Boyer, C.P., Galicki, K., Matzeu, P.: On eta-Einstein Sasakian geometry.Comm. Math. Phys. 262 (2006), 177–208. Zbl 1103.53022, MR 2200887, 10.1007/s00220-005-1459-6
Reference: [9] Bursztyn, H., Cavalcanti, G.R., Gualtieri, M.: Reduction of Courant algebroids and generalized complex structures.Adv. Math. 211 (2) (2007), 726–765. Zbl 1115.53056, MR 2323543, 10.1016/j.aim.2006.09.008
Reference: [10] Bursztyn, H., Cavalcanti, G.R., Gualtieri, M.: Generalized Kähler and hyper-Kähler quotients. Poisson geometry in mathematics and physics.Contemp. Math. 450 (2008), 61–77. MR 2397619, 10.1090/conm/450/08734
Reference: [11] Gates, S.J., Jr., , Hull, C.M., Rocek, M.: Twisted multiplets and new supersymmetric nonlinear sigma models.Nuclear Phys. B248 (1984), 157–186. MR 0776369
Reference: [12] Goto, R.: Deformations of generalized complex and generalized Kähler structures.J. Differential Geom. 84 (2010), 525–560. MR 2669364, 10.4310/jdg/1279114300
Reference: [13] Goto, R.: Unobstructed K-deformations of generalized complex structures and bi-Hermitian structures.Adv. Math. 231 (2012), 1041–1067. Zbl 1252.53095, MR 2955201, 10.1016/j.aim.2012.05.004
Reference: [14] Gualtieri, M.: Generalized complex geometry.Ph.D. thesis, University of Oxford, 2004, http://arxiv.org/abs/arXiv:math/0401221v1. MR 2811595
Reference: [15] Hitchin, N.: Instantons, Poisson structures and generalized Kähler geometry.Comm. Math. Phys. 265 (1) (2006), 131–164. Zbl 1110.53056, MR 2217300, 10.1007/s00220-006-1530-y
Reference: [16] Hitchin, N.: Bihermitian metrics on del Pezzo surfaces.J. Symplectic Geom. 5 (1) (2007), 1–8. MR 2371181, 10.4310/JSG.2007.v5.n1.a2
Reference: [17] Kenmotsu, K.: A class of almost contact Riemannian manifolds.Tôhoku Math. J. 24 (1972), 93–103. Zbl 0245.53040, MR 0319102, 10.2748/tmj/1178241594
Reference: [18] Lin, Y., Tolman, S.: Symmetries in generalized Kähler geometry.Comm. Math. Phys. (2006), 199–222. Zbl 1120.53049, MR 2249799, 10.1007/s00220-006-0096-z
Reference: [19] Marrero, J.C.: The local structure of trans-Sasakian manifolds.Ann. Mat. Pura Appl. (4) 162 (1) (1992), 77–86. Zbl 0772.53036, MR 1199647, 10.1007/BF01760000
Reference: [20] Olszak, Z.: Normal almost contact metric manifolds of dimension three.Ann. Polon. Math. (1986), 41–50. Zbl 0605.53018, MR 0859423, 10.4064/ap-47-1-41-50
Reference: [21] Oubiña, J.A.: New classes of almost contact metric structures.Publ. Math. Debrecen 32 (1985), 187–193. Zbl 0611.53032, MR 0834769
Reference: [22] Poon, Y.S., Wade, A.: Generalized contact structures.J. London Math. Soc. 83 (2) (2011), 333–352. Zbl 1226.53078, MR 2776640, 10.1112/jlms/jdq069
Reference: [23] Sekiya, K.: Generalized almost contact structures and generalized Sasakian structures.Osaka J. Math. 52 (2015), 303–306. Zbl 1325.53107, MR 3326601
Reference: [24] Tanno, S.: The topology of contact Riemannian manifolds.Illinois J. Math. 12 (1968), 700–717. Zbl 0165.24703, MR 0234486
Reference: [25] Tanno, S.: The automorphism groups of almost contact Riemannian manifolds.Tôhoku Math. J. 21 (1969), 21–38. Zbl 1168.51302, MR 0242094, 10.2748/tmj/1178243031
Reference: [26] Vaisman, I.: From generalized Kähler to generalized Sasakian structure.J. Geom. Symmetry Phyd. 18 (2010), 63–86. MR 2668883
Reference: [27] Yano, K., Kon, M.: Structures on manifolds.Series in Pure Math., vol. 3, World Scientific, 1984. Zbl 0557.53001, MR 0794310
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