Browse > Article
http://dx.doi.org/10.5831/HMJ.2019.41.3.539

𝜂-RICCI SOLITONS ON 𝜖 - LP-SASAKIAN MANIFOLDS WITH A QUARTER-SYMMETRIC METRIC CONNECTION  

Haseeb, Abdul (Department of Mathematics, Faculty of Science, Jazan University)
Prasad, Rajendra (Department of Mathematics and Astronomy, University of Lucknow)
Publication Information
Honam Mathematical Journal / v.41, no.3, 2019 , pp. 539-558 More about this Journal
Abstract
In this paper, we study ${\eta}$-Ricci solitons on ${\epsilon}$-LP-Sasakian manifolds with a quarter-symmetric metric connection satisfying certain curvature conditions. In particular, we have discussed that the Ricci soliton on ${\epsilon}$-LP-Sasakian manifolds with a quarter-symmetric metric connection satisfying certain curvature conditions is expanding or steady according to the vector field ${\xi}$ being timelike or spacelike. Moreover, we construct 3-dimensional examples of an ${\epsilon}$-LP-Sasakian manifold with a quarter-symmetric metric connection to verify some results of the paper.
Keywords
${\eta}$-Ricci solitons; ${\epsilon}$-LP-Sasakian; quarter-symmetric metric connection;
Citations & Related Records
연도 인용수 순위
  • Reference
1 A. Bejancu and K. L. Duggal, Real hypersurfaces of indefinite Kaehler manifolds, Int. J. Math. Math. Sci., 16 (1993), 545-556.   DOI
2 A. Haseeb, Some results on projective curvature tensor in an ${\epsilon}$-Kenmotsu manifold, Palestine J. Math., 6(Special Issue: II) (2017), 196-203.
3 A. Haseeb, A. Prakash and M. D. Siddiqi, On a quarter-symmetric metric connec- tion in an ${\epsilon}$-Lorentzian para-Sasakian manifold, Acta Math. Univ. Comenianae, 86(1) (2017), 143-152.
4 A. Haseeb, M. A. Khan. and M. D. Siddiqi, Some more results on an ${\epsilon}$-Kenmotsu manifold with a semi-symmetric metric connection, Acta Math. Univ. Comenianae, 85(1) (2016), 9-20.
5 A. Singh and S. Kishor, Some types of ${\eta}$-Ricci solitons on Lorentzian para-Sasakian manifolds, Facta Universitatis (NIS), 33(2) (2018), 217-230.
6 A. M. Blaga, ${\eta}$-Ricci solitons on Lorentzian para-Sasakian manifolds, Filomat, 30(2) (2016), 489-496.   DOI
7 B. O'Neill, Semi-Riemannian geometry with applications to relativity, Academic Press, New York-London, 1983.
8 D. G. Prakasha and B. S. Hadimani, ${\eta}$-Ricci solitons on para-Sasakian manifolds, J. Geom., 108 (2017), 383-392.   DOI
9 G. Perelman, Ricci flow with surgery on three manifolds, http://arXiv.org/abs/math/0303109, 2003, 1-22.
10 G. Perelman, The entropy formula for the Ricci flow and its geometric applications, http://arXiv.org/abs/math/0211159, 2002, 1-39.
11 J. T. Cho and M. Kimura, Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J., 61(2) (2009), 205-212.   DOI
12 K. Mandal and U. C. De, Quarter-symmetric metric connection in a P-Sasakian manifold, Analele Univ. de Vest, Timisoara Seria Matematica-Informatica, LIII(1) (2015), 137-150.
13 K. Yano and M. Kon, Structures on Manifolds, Series in Pure Math., Vol. 3, World Sci., 1984.
14 M. Ahmad, J. B. Jun, and A. Haseeb, Hypersurfaces of almost r-paracontact Riemannian manifold with a quarter symmetric metric connection, Bull. Korean Math. Soc., 46(3) (2009), 477-487.   DOI
15 M. Ali and Z. Ahsan, Gravitational field of Schwarzschild soliton, Arab J. Math. Sci., 21 (2015), 15-21.   DOI
16 R. N. Singh and S. K. Pandey, On quarter-symmetric metric connection in an LP-Sasakian manifold, Thai J. Math., 12 (2014), 357-371.
17 M. M. Tripathi, E. Kilic, S. Y. Perktas and S. Keles, Indefinite almost para-contact metric manifolds, Int. J. Math. and Math. Sci., (2010), Article ID: 846195, 19 pages.
18 R. Prasad and A. Haseeb, Conformal curvature tensor on K-contact manifolds with respect to the quarter symmetric metric connection, Facta Universitatis (NIS), Ser. Math. Inform., 32 (2017), 503-514.
19 R. Prasad and V. Srivastava, On ${\epsilon}$-Lorentzian para-Sasakian manifolds, Commun. Korean Math. Soc., 27 (2012), 297-306.   DOI
20 R. Sharma, Certain results on K-contact and (K,${\mu}$)-contact manifolds, J. Geom., 89 (2008), 138-147.   DOI
21 R. N. Singh, S. K. Pandey, G. Pandey and K. Tiwari, On a semi-symmetric metric connection in an ${\epsilon}$-Kenmotsu manifold, Commun. Korean Math. Soc., 29 (2014), 331-343.   DOI
22 R. S. Hamilton, The Ricci flow on surfaces, Mathematics and general relativity, Contemp. Math., 71, American Math. Soc., (1988), 237-262.
23 R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Diff. Geom., 17 (1982), 255-306.   DOI
24 S. Deshmukh, H. Alodan and H. Al-Sodais, A note on Ricci solitons, Balkan J. Geom. Appl., 16 (2011), 48-55.
25 S. Golab, On semi-symmetric and quarter-symmetric linear connections, Tensor (N.S.), 29(1975), 249-254.
26 U. C. De, Ricci soliton and gradient Ricci soliton on P-Sasakian manifolds, The Aligarh Bull. of Maths., 29 (2010), 29-34.
27 U. C. De and A. Sarkar, On ${\epsilon}$-Kenmotsu manifold, Hardonic J., 32 (2009), 231-242.
28 X. Xufeng and C. Xiaoli, Two theorems on ${\epsilon}$-Sasakian manifolds, Int. J. Math. Math. Sci., 21 (1998), 249-54.   DOI
29 U. C. De and A. K. Mondal, Quarter-symmetric metric connection on 3-dimensional quasi-Sasakian manifolds, SUT J. Math., 46 (2010), 35-52.