Some characterizations of property of trans-Sasakian 3-manifolds
-
Yan Zhao
Abstract
In this paper, we obtain some characterizations on the Reeb vector field for a trans-Sasakian manifold to be proper.
This work was supported by the Doctoral Foundation of Henan University of Technology (No. 2018BS061).
(Communicated by Július Korbaš )
References
[1] Blair, D. E.: Riemannian Geometry of Contact and Symplectic Manifolds. Progr. Math. 203, Birkäuser, 2010.10.1007/978-0-8176-4959-3Search in Google Scholar
[2] Chen, X.—Wu, G.: Remarks on Ricci solitons in trans-Sakian manifolds, J. Math. (PRC) 34 (2014), 603–609.Search in Google Scholar
[3] Chinea, D.—Gonzalez, C.: A classification of almost contact metric manifolds, Ann. Mat. Pura Appl. 156 (1990), 15–36.10.1007/BF01766972Search in Google Scholar
[4] Cho, J. T.: Notes on contact Ricci solitons, Proc. Edinb. Math. Soc. 54 (2011), 47–53.10.1017/S0013091509000571Search in Google Scholar
[5] Cho, J. T.—Kimura, M.: Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J. 61 (2009), 205–212.10.2748/tmj/1245849443Search in Google Scholar
[6] De, U. C.–De, K.: On a class of three-dimensional trans-Sasakian manifolds, Commun. Korean Math. Soc. 27 (2012), 795–808.10.4134/CKMS.2012.27.4.795Search in Google Scholar
[7] De, U. C.—Mondal, A. K.: On 3-dimensional normal almost contact metric manifolds satisfying certain curvature conditions, Commun. Korean Math. Soc. 24 (2009), 265–275.10.4134/CKMS.2009.24.2.265Search in Google Scholar
[8] 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.Search in Google Scholar
[9] De, U. C.—Tripathi, M. M.: Ricci tensor in 3-dimensional trans-Sasakian manifolds, Kyungpook Math. J. 43 (2003), 247–255.Search in Google Scholar
[10] Deshmukh, S.: Trans-Sasakian manifolds homothetic to Sasakian manifolds, Mediterr. J. Math. 13 (2016), 2951–2958.10.1007/s00009-015-0666-4Search in Google Scholar
[11] Deshmukh, S.: Geometry of 3-dimensional trans-Sasakaian manifolds, An. Stiint. Univ. Al. I. Cuza Iasi Mat. (N.S.) 63 (2016), 183–192.10.2478/aicu-2014-0025Search in Google Scholar
[12] Deshmukh, S.—Al-Solamy, F.: A Note on compact trans-Sasakian manifolds, Mediterr. J. Math. 13 (2016), 2099–2104.10.1007/s00009-015-0582-7Search in Google Scholar
[13] Deshmukh, S.—Tripathi, M. M.: A Note on compact trans-Sasakian manifolds, Math. Slovaca 63 (2013), 1361–1370.10.1007/s00009-015-0582-7Search in Google Scholar
[14] Duggal, K. L.: Affine conformal vector fields in semi-Riemannian manifolds, Acta Appl. Math. 23 (1991), 275–294.10.1007/BF00047139Search in Google Scholar
[15] Hinterleitner, I.—Kiosak, V. A.: φ(Ric)-vector fields in Riemannian spaces, Arc. Math. (Brno) 44 (2008), 385–390.10.1063/1.3275604Search in Google Scholar
[16] Kim, T. W.—Pak, H. K.: Canonical foliations of certain classes of almost contact metric structures, Acta Math. Sinica (Engl. Ser.) 21 (2015), 841–846.10.1007/s10114-004-0520-2Search in Google Scholar
[17] Marrero, J. C.: The local structure of trans-Sasakian manifolds, Ann. Mat. Pura Appl. 162 (1992), 77–86.10.1007/BF01760000Search in Google Scholar
[18] Okumura, K.: Certain almost contact hypersurfaces in Kaehlerian manifolds of constant holomorphic sectional curvatures, Tohoku Math. J. 16 (1964), 270–284.10.2748/tmj/1178243673Search in Google Scholar
[19] Oprea, T.: 2-Killing vector fields on Riemannian manifolds, Balkan J. Geom. Appl. 13 (2008), 87–92.Search in Google Scholar
[20] Oubiña, A.: New classes of almost contact metric structures, Publ. Math. Debrecen 32 (1985), 187–193.10.5486/PMD.1985.32.3-4.07Search in Google Scholar
[21] Perelman, G.: The entropy formula for the Ricci flow and its geometric applications, 2002, arXiv: math.DG/02111159Search in Google Scholar
[22] Wang, W.—Liu, X.: Ricci tensors on trans-Sasakian 3-manifolds, Filomat 32 (2018), 4365–4374.10.2298/FIL1812365WSearch in Google Scholar
[23] Wang, Y.: Ricci solitons on 3-dimensional cosymplectic manifolds, Math. Slovaca 67 (2017), 979–984.10.1515/ms-2017-0026Search in Google Scholar
[24] Wang, Y.: Minimal and harmonic Reeb vector fields on trans-Sasakian 3-manifolds, J. Korean Math. Soc. 55 (2018), 1321–1336.Search in Google Scholar
[25] Wang, Y.—Wang, W.: A remark on trans-Sasakian 3-manifolds, Rev. Union Mat. Argentina 60 (2019), 257–264.10.33044/revuma.v60n1a16Search in Google Scholar
[26] Yano, K.: Integral Formulas in Riemannian Geometry. Pure and Applied Mathematics, No. 1, Marcel Dekker, New York, 1970.Search in Google Scholar
[27] Zhao, Y.: Ricciη-parallel trans-Sasakian 3-manifolds, Quaest. Math. 44 (2021), 7–15.10.2989/16073606.2019.1657980Search in Google Scholar
© 2021 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Regular papers
- Prof. RNDr. Michal Fečkan, DrSc. – Sexagenarian?
- Tribonacci numbers with two blocks of repdigits
- Padovan numbers that are concatenations of two distinct repdigits
- On the 2-rank and 4-rank of the class group of some real pure quartic number fields
- A general inverse matrix series relation and associated polynomials – II
- Some hardy type inequalities with finsler norms
- Starlikeness and convexity of the product of certain multivalent functions with higher-order derivatives
- Block Hessenberg matrices and spectral transformations for matrix orthogonal polynomials on the unit circle
- How is the period of a simple pendulum growing with increasing amplitude?
- Fourier transforms of convolution operators on orlicz spaces
- Some characterizations of property of trans-Sasakian 3-manifolds
- P-Adic metric preserving functions and their analogues
- On statistical convergence of sequences of closed sets in metric spaces
- A characterization of the uniform convergence points set of some convergent sequence of functions
- A nonparametric estimation of the conditional ageing intensity function in censored data: A local linear approach
- Donsker’s fuzzy invariance principle under the Lindeberg condition
- Characterization of generalized Gamma-Lindley distribution using truncated moments of order statistics
- Matrix variate pareto distributions
- Global exponential periodicity and stability of neural network models with generalized piecewise constant delay
- Optimal inequalities for contact CR-submanifolds in almost contact metric manifolds
Articles in the same Issue
- Regular papers
- Prof. RNDr. Michal Fečkan, DrSc. – Sexagenarian?
- Tribonacci numbers with two blocks of repdigits
- Padovan numbers that are concatenations of two distinct repdigits
- On the 2-rank and 4-rank of the class group of some real pure quartic number fields
- A general inverse matrix series relation and associated polynomials – II
- Some hardy type inequalities with finsler norms
- Starlikeness and convexity of the product of certain multivalent functions with higher-order derivatives
- Block Hessenberg matrices and spectral transformations for matrix orthogonal polynomials on the unit circle
- How is the period of a simple pendulum growing with increasing amplitude?
- Fourier transforms of convolution operators on orlicz spaces
- Some characterizations of property of trans-Sasakian 3-manifolds
- P-Adic metric preserving functions and their analogues
- On statistical convergence of sequences of closed sets in metric spaces
- A characterization of the uniform convergence points set of some convergent sequence of functions
- A nonparametric estimation of the conditional ageing intensity function in censored data: A local linear approach
- Donsker’s fuzzy invariance principle under the Lindeberg condition
- Characterization of generalized Gamma-Lindley distribution using truncated moments of order statistics
- Matrix variate pareto distributions
- Global exponential periodicity and stability of neural network models with generalized piecewise constant delay
- Optimal inequalities for contact CR-submanifolds in almost contact metric manifolds
