Glasnik Matematicki, Vol. 53, No. 1 (2018), 205-220.

η-RICCI SOLITONS IN (ε)-ALMOST PARACONTACT METRIC MANIFOLDS

Adara Monica Blaga, Selcen Yüksel Perktaş, Bilal Eftal Acet and Feyza Esra Erdoğan

Department of Mathematics, West University of Timişoara, 300223 Timişoara, România
e-mail: adarablaga@yahoo.com

Department of Mathematics, Adıyaman University, 02040 Adıyaman, Turkey
e-mail: sperktas@adiyaman.edu.tr

Department of Mathematics, Adıyaman University, 02040 Adıyaman, Turkey
e-mail: eacet@adiyaman.edu.tr

Department of Elementary Education, Adıyaman University, 02040 Adıyaman, Turkey
e-mail: ferdogan@adiyaman.edu.tr


Abstract.   The object of this paper is to study η -Ricci solitons on ( ε ) -almost paracontact metric manifolds. We investigate η -Ricci solitons in the case when its potential vector field is exactly the characteristic vector field ξ of the ( ε ) -almost paracontact metric manifold and when the potential vector field is torse-forming. We also study Einstein-like and ( ε )-para Sasakian manifolds admitting η-Ricci solitons. Finally we obtain some results for η -Ricci solitons on ( ε )-almost paracontact metric manifolds with a special view towards parallel symmetric (0,2) -tensor fields.

2010 Mathematics Subject Classification.   53C15, 53C25, 53C40, 53C42, 53C50.

Key words and phrases.   ( ε ) -almost paracontact metric manifold, ( ε ) -para Sasakian manifold, Einstein-like manifold, η -Ricci soliton.


Full text (PDF) (free access)

DOI: 10.3336/gm.53.1.14


References:

  1. M. M. Akbar and E. Woolgar, Ricci solitons and Einstein-scalar field theory, Classical Quantum Gravity 26 (2009), 055015, 14pp.
    MathSciNet     CrossRef

  2. A. Bejancu and K. L. Duggal, Real hypersurfaces of indefinite Kaehler manifolds, Internat. J. Math. Math. Sci. 16 (1993), 545-556.
    MathSciNet     CrossRef

  3. A. M. Blaga, η-Ricci solitons on Lorentzian para-Sasakian manifolds, Filomat 30 (2016), 489-496.
    MathSciNet     CrossRef

  4. A. M. Blaga, η-Ricci solitons on para-Kenmotsu manifolds, Balkan J. Geom. Appl. 20 (2015), 1-13.
    MathSciNet    

  5. A. M. Blaga and M. Crasmareanu, Torse-forming η-Ricci solitons in almost paracontact η-Einstein geometry, Filomat 31 (2017), 499-504.
    MathSciNet     CrossRef

  6. M. Brozos-Vazquez, G. Calvaruso, E. Garcia-Rio and S. Gavino-Fernandez, Three-dimensional Lorentzian homogeneous Ricci solitons, Israel J. Math. 188 (2012), 385-403.
    MathSciNet     CrossRef

  7. C. Calin and M. Crasmareanu, η-Ricci solitons on Hopf Hypersurfaces in complex space forms, Rev. Roumaine Math. Pures Appl. 57 (2012), 55-63.
    MathSciNet    

  8. J. S. Case, Singularity theorems and the Lorentzian splitting theorem for the Bakry Emery Ricci tensor, J. Geom. Phys. 60 (2010), 477-490.
    MathSciNet     CrossRef

  9. J. T. Cho and M. Kimura, Ricci solitons and real hypersurfaces in a complex space form, Tôhoku Math. J. (2) 61 (2009), 205-212.
    MathSciNet     CrossRef

  10. U. C. De, Second order parallel tensors on P-Sasakian manifolds, Publ. Math. Debrecen 49 (1996), 33-37.
    MathSciNet    

  11. L. P. Eisenhart, Symmetric tensors of the second order whose first covariant derivatives are zero, Trans. Amer. Math. Soc. 25 (1923), 297-306.
    MathSciNet     CrossRef

  12. D. H. Friedan, Nonlinear models in 2+ε dimensions, Ann. Phys. 163 (1985), 318-419.
    MathSciNet     CrossRef

  13. R. S. Hamilton, The Ricci flow on surfaces, in: Mathematics and general relativity, Amer. Math. Soc. Providence, 1988, 237-262.
    MathSciNet     CrossRef

  14. R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), 255-306.
    MathSciNet     CrossRef

  15. H. Levy, Symmetric tensors of the second order whose covariant derivatives vanish, Ann. of Math. (2) 27 (1925), 91-98.
    MathSciNet     CrossRef

  16. Z. Li, Second order parallel tensors on P-Sasakian manifolds with a coefficient k, Soochow J. Math. 23 (1997), 97-102.
    MathSciNet    

  17. K. Matsumoto, On Lorentzian paracontact manifolds, Bull. Yamagata Univ. Natur. Sci. 12 (1989), 151-156.
    MathSciNet    

  18. S. Sasaki, On differentiable manifolds with certain structures which are closely related to almost contact structure I, Tôhoku Math. J. (2) 12 (1960), 459-476.
    MathSciNet     CrossRef

  19. I. Satō, On a structure similar to the almost contact structure, Tensor (N.S.) 30 (1976), 219-224.
    MathSciNet    

  20. R. Sharma, On Einstein-like p-Sasakian manifold, Mat. Vesnik 6(19)(34) (1982), 177-184.
    MathSciNet    

  21. R. Sharma, Second order parallel tensor in real and complex space forms, Internat. J. Math. Math. Sci. 12 (1989), 787-790.
    MathSciNet     CrossRef

  22. R. Sharma, Second order parallel tensors on contact manifolds, Algebras Groups Geom. 7 (1990), 145-152.
    MathSciNet    

  23. R. Sharma, Second order parallel tensors on contact manifolds. II, C. R. Math. Rep. Acad. Sci. Canada 13 (1991), 259-264.
    MathSciNet    

  24. T. Takahashi, Sasakian manifold with pseudo-Riemannian metric, Tôhoku Math. J. (2) 21 (1969), 271-290.
    MathSciNet     CrossRef

  25. M. M. Tripathi, E. Kılıç, S. Y. Perktaş and S. Keleş, Indefinite almost paracontact metric manifolds, Int. J. Math. Math. Sci. (2010), 846195, 19 pp.
    MathSciNet     CrossRef

  26. S. Y. Perktaş, E. Kılıç, M. M. Tripathi, and S. Keleş, On (ε )-para Sasakian 3-manifolds, Int. J. Pure Appl. Math. 77 (2012), 485-499.
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