| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2017-03-23T10:05:45Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146074 |
| . |
| 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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