About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Bouzir, Habib ; Beldjilali, Gherici ; Belkhelfa, Mohamed ; Wade, Aissa
Generalized Kählerian manifolds and transformation of generalized contact structures. (English). Archivum Mathematicum, vol. 53 (2017), issue 1, pp. 35-48
MSC: 53C10, 53C15, 53C18, 53D25 | MR 3636680 | Zbl 06738497 | DOI: 10.5817/AM2017-1-35
Keywords:
product manifolds; trans-Sasakian manifolds; generalized Kählerian manifolds; generalized contact structures; transformation of generalized almost contact structures; generalized almost complex structures
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.
References:
[1] Apostolov, V., Gualtieri, M.: Generalized Kähler manifolds, commuting complex structures, and split tangent bundles. Comm. Math. Phys. 2 (2007), 561–575. DOI 10.1007/s00220-007-0196-4 | MR 2287917 | Zbl 1135.53018
[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. MR 0662851 | Zbl 0491.53047
[3] Beldjilali, G., Belkhelfa, M.: Kählerian structures and $\mathcal{D}$-homothetic Bi-warping. J. Geom. Symmetry Phys. 42 (2016), 1–13. MR 3586441
[4] Blair, D.E.: Contact manifolds in Riemannian geometry. Lecture Notes in Mathematics, vol. 509, Springer, 1976, pp. 17–35. MR 0467588 | Zbl 0319.53026
[5] Blair, D.E.: Riemannian geometry of contact and symplectic manifolds. Progress in Mathematics, vol. 203, Birkhäuser Boston, 2002. MR 1874240 | Zbl 1011.53001
[6] Blair, D.E.: $\mathcal{D}$-homothetic warping. Publ. Inst. Math. (Beograd) (N.S.) 94 (108) (2013), 47–54. DOI 10.2298/PIM1308047B | MR 3137489
[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. DOI 10.5565/PUBLMAT_34190_15 | MR 1059874 | Zbl 0721.53035
[8] Boyer, C.P., Galicki, K., Matzeu, P.: On eta-Einstein Sasakian geometry. Comm. Math. Phys. 262 (2006), 177–208. DOI 10.1007/s00220-005-1459-6 | MR 2200887 | Zbl 1103.53022
[9] Bursztyn, H., Cavalcanti, G.R., Gualtieri, M.: Reduction of Courant algebroids and generalized complex structures. Adv. Math. 211 (2) (2007), 726–765. DOI 10.1016/j.aim.2006.09.008 | MR 2323543 | Zbl 1115.53056
[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. DOI 10.1090/conm/450/08734 | MR 2397619
[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
[12] Goto, R.: Deformations of generalized complex and generalized Kähler structures. J. Differential Geom. 84 (2010), 525–560. DOI 10.4310/jdg/1279114300 | MR 2669364
[13] Goto, R.: Unobstructed K-deformations of generalized complex structures and bi-Hermitian structures. Adv. Math. 231 (2012), 1041–1067. DOI 10.1016/j.aim.2012.05.004 | MR 2955201 | Zbl 1252.53095
[14] Gualtieri, M.: Generalized complex geometry. Ph.D. thesis, University of Oxford, 2004, http://arxiv.org/abs/arXiv:math/0401221v1 MR 2811595
[15] Hitchin, N.: Instantons, Poisson structures and generalized Kähler geometry. Comm. Math. Phys. 265 (1) (2006), 131–164. DOI 10.1007/s00220-006-1530-y | MR 2217300 | Zbl 1110.53056
[16] Hitchin, N.: Bihermitian metrics on del Pezzo surfaces. J. Symplectic Geom. 5 (1) (2007), 1–8. DOI 10.4310/JSG.2007.v5.n1.a2 | MR 2371181
[17] Kenmotsu, K.: A class of almost contact Riemannian manifolds. Tôhoku Math. J. 24 (1972), 93–103. DOI 10.2748/tmj/1178241594 | MR 0319102 | Zbl 0245.53040
[18] Lin, Y., Tolman, S.: Symmetries in generalized Kähler geometry. Comm. Math. Phys. (2006), 199–222. DOI 10.1007/s00220-006-0096-z | MR 2249799 | Zbl 1120.53049
[19] Marrero, J.C.: The local structure of trans-Sasakian manifolds. Ann. Mat. Pura Appl. (4) 162 (1) (1992), 77–86. DOI 10.1007/BF01760000 | MR 1199647 | Zbl 0772.53036
[20] Olszak, Z.: Normal almost contact metric manifolds of dimension three. Ann. Polon. Math. (1986), 41–50. DOI 10.4064/ap-47-1-41-50 | MR 0859423 | Zbl 0605.53018
[21] Oubiña, J.A.: New classes of almost contact metric structures. Publ. Math. Debrecen 32 (1985), 187–193. MR 0834769 | Zbl 0611.53032
[22] Poon, Y.S., Wade, A.: Generalized contact structures. J. London Math. Soc. 83 (2) (2011), 333–352. DOI 10.1112/jlms/jdq069 | MR 2776640 | Zbl 1226.53078
[23] Sekiya, K.: Generalized almost contact structures and generalized Sasakian structures. Osaka J. Math. 52 (2015), 303–306. MR 3326601 | Zbl 1325.53107
[24] Tanno, S.: The topology of contact Riemannian manifolds. Illinois J. Math. 12 (1968), 700–717. MR 0234486 | Zbl 0165.24703
[25] Tanno, S.: The automorphism groups of almost contact Riemannian manifolds. Tôhoku Math. J. 21 (1969), 21–38. DOI 10.2748/tmj/1178243031 | MR 0242094 | Zbl 1168.51302
[26] Vaisman, I.: From generalized Kähler to generalized Sasakian structure. J. Geom. Symmetry Phyd. 18 (2010), 63–86. MR 2668883
[27] Yano, K., Kon, M.: Structures on manifolds. Series in Pure Math., vol. 3, World Scientific, 1984. MR 0794310 | Zbl 0557.53001
Partner of
EuDML logo