Reeb flow invariant ∗-Ricci operators on trans-Sasakian three-manifolds
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Rongsheng Ma
Abstract
In this paper, we investigate the ∗-Ricci operators on trans-Sasakian three-manifolds. We find conditions at which ∗- Ricci tensor on trans-Sasakian three-manifolds is symmetric and under which the ∗-Ricci operators are Reeb flow invariant.
This work was supported by National Natural Science Foundation of China Grant No. 11671070
Acknowledgement
The authors wish to express their sincere thanks to the referee for helpful comments to improve the original manuscript.
(Communicated by Július Korbaš )
References
[1] Blair, D. E.: Riemannian Geometry of Contact and Symplectic Manifolds, 2nd ed., Birkhäuser Boston, Inc., Boston, MA, 2010.10.1007/978-0-8176-4959-3Suche in Google Scholar
[2] Cho, J. T.: Contact 3-manifolds with the Reeb flow symmetry, Tohoku Math. J. 66 (2014), 491–500.10.2748/tmj/1432229193Suche in Google Scholar
[3] Cho, J. T.: Reeb flow symmetry on almost cosymplectic three-manifolds, Bull. Korean Math. Soc. 53 (2016), 1249–1257.10.4134/BKMS.b150656Suche in Google Scholar
[4] Cho, J. T.—Chun, S. H.: Unit tangent sphere bundles with the Reeb flow invariant Ricci operator, Kodai Math. J. 40 (2017), 102–116.10.2996/kmj/1490083226Suche in Google Scholar
[5] Cho, J. T.—Ichi Inoguchi, J.: Onφ-Einstein contact riemannian manifolds, Mediterr. J. Math. 7 (2010), 143–167.10.1007/s00009-010-0049-9Suche in Google Scholar
[6] Cho, J. T.—Kimura, M.: Reeb flow symmetry on almost contact three-manifolds, Differential Geom. Appl. 35 (2014), 266–273.10.1016/j.difgeo.2014.05.002Suche in Google Scholar
[7] De, U. C.—Mondal, A. K.: The structure of some classes of 3-dimensional normal almost contact metric manifolds, Bull. Malays. Math. Sci. Soc. 36 (2013), 501–509.Suche in Google Scholar
[8] Deshmukh, S.: Trans-Sasakian manifolds homothetic to Sasakian manifolds, Mediterr. J. Math. 13 (2016), 2951–2958.10.1007/s00009-015-0666-4Suche in Google Scholar
[9] Deshmukh, S.—Al-Solamy, F.: A note on compact trans-Sasakian manifolds, Mediterr. J. Math. 13 (2016), 2099–2104.10.1007/s00009-015-0582-7Suche in Google Scholar
[10] Deshmukh, S.—Tripathi, M. M.: A note on trans-Sasakian manifolds, Math. Slovaca 63 (2013), 1361–1370.10.2478/s12175-013-0176-4Suche in Google Scholar
[11] Desmukh, S.—De, U. C.—Al-Solamy, F.: Trans-Sasakian manifolds homothetic to Sasakian manifolds, Publ. Math. Debrecen 88 (2016), 439–448.10.5486/PMD.2016.7398Suche in Google Scholar
[12] Ghosh, A.—Patra, D. S.: *-Ricci soliton within the frame-work of Sasakian and (κ, μ)-contact manifold, Int. J. Geom. Methods Mod. Phys. 15 (2018), Art. ID 1850120.10.1142/S0219887818501207Suche in Google Scholar
[13] Hamada, T.: Real hypersurfaces of complex space forms in terms of Ricci ∗-tensor, Tokyo J. Math. 25 (2002), 473–483.10.3836/tjm/1244208866Suche in Google Scholar
[14] Kaimakamis, G.—Panagiotidou, K.: *-Ricci solitons of real hypersurfaces in non-flat complex space forms, J. Geom. Phys. 86 (2014), 408–413.10.1016/j.geomphys.2014.09.004Suche in Google Scholar
[15] Ma, R.—Pei, D.: Some curvature properties on Lorentzian generalized Sasakian-space-forms, Adv. Math. Phys. (2019), Art. ID 5136758.10.1155/2019/5136758Suche in Google Scholar
[16] Marrero, J. C.: The local structure of trans-Sasakian manifolds, Ann. Mat. Pura Appl. 162 (1992), 77–86.10.1007/BF01760000Suche in Google Scholar
[17] Olszak, Z.: Curvature properties of quasi-Sasakian manifolds, Tensor (N.S.) 38 (1982), 19–28.Suche in Google Scholar
[18] Olszak, Z.: On three-dimensional conformally flat quasi-Sasakian manifolds, Period. Math. Hungar. 33 (1996), 105–113.10.1007/BF02093508Suche in Google Scholar
[19] Tachibana, S.-I.: On almost-analytic vectors in certain almost-Hermitian manifolds, Tohoku Math. J. 11 (1959), 351–363.10.2748/tmj/1178244533Suche in Google Scholar
[20] Tanno, S.: Quasi-Sasakian structures of rank 2p + 1, J. Differ. Geom. 5 (1971), 317–324.10.4310/jdg/1214429995Suche in Google Scholar
[21] Wang, W.—Liu, X.: Ricci tensors on trans-sasakian 3-manifolds, Filomat 32 (2018), 4365–4374.10.2298/FIL1812365WSuche in Google Scholar
[22] Wang, Y.: Minimal and harmonic Reeb vector fields on trans-Sasakian 3-manifolds, J. Korean Math. Soc. 55 (2018), 1321–1336.Suche in Google Scholar
[23] Zhao, Y.—Wang, W.—Liu, X.: Trans-sasakian 3-manifolds with reeb flow invariant ricci operator. Mathematics 6 (2018), 246.10.3390/math6110246Suche in Google Scholar
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Artikel in diesem Heft
- Regular papers
- Properties of implication in effect algebras
- On a nonlinear relation for computing the overpartition function
- Six-cycle systems
- Representation of bifinite domains by BF-closure spaces
- L-fuzzy cosets in universal algebras
- Density of sets with missing differences and applications
- Degree of independence of numbers
- A generalization of a result on the sum of element orders of a finite group
- A New fuzzy McShane integrability
- Hankel determinants of second and third order for the class 𝓢 of univalent functions
- Herglotz's theorem for Jacobi-Dunkl positive definite sequences
- Functional inequalities for Gaussian hypergeometric function and generalized elliptic integral of the first kind
- Existence on solutions of a class of casual differential equations on a time scale
- On a general system of difference equations defined by homogeneous functions
- Jordan amenability of banach algebras
- A new notion of orthogonality involving area and length
- Reeb flow invariant ∗-Ricci operators on trans-Sasakian three-manifolds
- A finite graph is homeomorphic to the Reeb graph of a Morse–Bott function
- On first countable quasitopological homotopy groups
