On eta-Einstein N(k)-contact metric manifolds
DOI:
https://doi.org/10.5269/bspm.46872Abstract
The aim of this paper is to characterize eta-Einstein N(k)-contact metric manifolds admits eta-Ricci soliton. Several consequences of this result are discussed. Beside these, we also study eta-Einstein N(k)-contact metric manifolds satisfying certain curvature conditions. Among others it is shown that such a manifold is either locally isometric to the Riemannian product En+1(0) Sn(4) or a Sasakian manifold. Finally, we construct an example to verify some results.
References
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24. Yadav, S. K.,Chaubey, S. K., Suthar, D. L.Some results onη-Ricci solitons on(LCS)n-manifolds, Surveys in Mathe-matics and its Applications, 13, 237-250, (2018).
25. Yadav, S. K., Chaubey, S. K., Suthar, D. L.Some geometric properties ofη-Ricci solitons and gradient Ricci solitonson(LCS)n-manifolds, CUBO A Mathematical Journal, 2(19), 33-48 (2017). https://doi.org/10.4067/S0719-06462017000200033
26. Yadav, S. K.,Ricci solitons on Para-Kaehler manifolds, Extracta Mathematikae, 34(2), 269-284, (2019).
27. Yadav, S. K., Ozturk, H.,On(ǫ)-Almost paracontact metric manifolds with conformalη-Ricci soliton, DifferentialGeometry-Dynamical Systems, 19, 1-10,(2019).
28. Yadav, S. K., Kushwaha, A., Narain, D.,Certain results forη-Ricci soliton and Yamabe soliton on quasi-Sasakian3-manifolds, Cubo A mathematical Journal, 21(2), 77-98, (2019). https://doi.org/10.4067/S0719-06462019000200077
29. Yadav, S. K., Chaubey, S. K., Suthar, D.L.,Certain geometric properties ofη-Ricci soliton onη-Einstein Para-Kenmotsumanifolds, Palestine Journal of Mathematics, 9(1), 237-244, (2020).
2. Blair, D. E.,Two remarks on contact metric structure, Tohoku Math. J., 29, 319-324, (1977). https://doi.org/10.2748/tmj/1178240602
3. Blair, D. E., Koufogiorgos, T., Papantoniou, B. J.,Contact metric manifolds satisfying a nullity condition, Israel J. ofMath., 19, 189-214, (1995). https://doi.org/10.1007/BF02761646
4. Blaga, A. M.,η-Ricci solitons on para-Kenmotsu, manifolds, arXiv:1402.0223v1, [math DG], (2014).
5. Blair, D. E., Kim, J. S., Tripathi, M. M.,On the concircular curvature tensor of a contact metric manifold, J. KoreanMath. Soc. 42, 883-892, (2005). https://doi.org/10.4134/JKMS.2005.42.5.883
6. Boeckx, E.A full classification of contact metric(κ, μ)-spaces, Illinois J. Math., 44(1), 212-219, (2000). https://doi.org/10.1215/ijm/1255984960
7. Cecil, T. E., Ryan, P. J.,Focal sets and real hypersurfaces in complex projective space, Trans. Amer. Math. Soc., 269,481-499, (1982). https://doi.org/10.2307/1998460
8. Cho, J. T., Kimura, M.,Ricci solitons and Real hypersurfaces in a complex space form, Tohoku math. J., 61, 205-212,(2009). https://doi.org/10.2748/tmj/1245849443
9. Hamilton, R. S.,The Ricci flow on surfaces, Mathematical and general relativity(Santa Cruz,CA,1986), AmericanMath. Soc., Contemp. Math., 71, 237-262, (1988). https://doi.org/10.1090/conm/071/954419
10. Ki, U-H.,Real hypersurfaces with parallel Ricci tensor of a complex space form, Tsukaba J. Math., 13, 73-81, (1989). https://doi.org/10.21099/tkbjm/1496161007
11. Hui, S. K., Yadav, S. K., Chaubey, S. K.η-Ricci soliton on3-dimensionalf-Kenmotsu manifolds, Appl. Appl. Math.,13(2), 933-951, (2018).
12. Hui, S. K., Yadav, S. K., Patra, A.Almost conformal Ricci soliton onf-Kenmotsu manifolds, Khayam J. Math., 5(1),89-104, (2019).
13. Montiel, S.,Real hypersurfaces of complex hyperbolic space, J.Math. Soc. Japan, 35, 515-535, (1985). https://doi.org/10.2969/jmsj/03730515
14. Mikes, J., Rachånek, L.,Torse forming vector fields inT-semisymmetric Riemannian spaces. In: Steps in Diff. Geom.,Proc. of the Colloquium on Diff. Geom., Univ. Debrecen, Debrecen, Hungary, 219-229, (2000).
15. Mikes, J. et al.,Differential Geometry of Special Mappings, Palacky Univ. Press, Olomouc, (2015).
16. Nagaraja, H. G., Prematha, C. R.,Ricci solitons in Kenmotsu manifolds, Journal of Mathematical analysis, 3 (2),18-24, (2012).
17. Prakasha, D. G., Hadimani, B. S.,η-Ricci solitons on para-Sasakian manifolds, J. Geom.,DOI 10.1007/s00022-016-0345-z.
18. Pokhariyal, G. P., Mishra, R. S.,The curvature tensor and their relativistic significance, Yokohama Math. J., 18,105-108, (1970).
19. Pokhariyal, G. P., Yadav, S. K., Chaubey, S. K.Ricci solitons on trans-Sasakian manifolds, Diff. Geom. and Dyn. Sys.20, 138-158, (2018).
20. Sharma, R.,Certain results onK-contact and(κ, μ)-contact manifolds, J.Geom., 89, 138-147, (2008). https://doi.org/10.1007/s00022-008-2004-5
21. Shaikh, A. A., Baishya, K. K.,On(k, μ)-contact metric manifolds, J. Diff. Geom. and Dyn. Sys., 11, 253-261, (1906).
22. Tanno, S.,Ricci curvatures of contact Riemannian manifolds, Tohoku Math. J., 40, 441-448, (1988). https://doi.org/10.2748/tmj/1178227985
23. Tripathi, M. M.,Ricci solitons in contact metric manifolds, arXiv:0801, 4222v1, [math DG], (2008).
24. Yadav, S. K.,Chaubey, S. K., Suthar, D. L.Some results onη-Ricci solitons on(LCS)n-manifolds, Surveys in Mathe-matics and its Applications, 13, 237-250, (2018).
25. Yadav, S. K., Chaubey, S. K., Suthar, D. L.Some geometric properties ofη-Ricci solitons and gradient Ricci solitonson(LCS)n-manifolds, CUBO A Mathematical Journal, 2(19), 33-48 (2017). https://doi.org/10.4067/S0719-06462017000200033
26. Yadav, S. K.,Ricci solitons on Para-Kaehler manifolds, Extracta Mathematikae, 34(2), 269-284, (2019).
27. Yadav, S. K., Ozturk, H.,On(ǫ)-Almost paracontact metric manifolds with conformalη-Ricci soliton, DifferentialGeometry-Dynamical Systems, 19, 1-10,(2019).
28. Yadav, S. K., Kushwaha, A., Narain, D.,Certain results forη-Ricci soliton and Yamabe soliton on quasi-Sasakian3-manifolds, Cubo A mathematical Journal, 21(2), 77-98, (2019). https://doi.org/10.4067/S0719-06462019000200077
29. Yadav, S. K., Chaubey, S. K., Suthar, D.L.,Certain geometric properties ofη-Ricci soliton onη-Einstein Para-Kenmotsumanifolds, Palestine Journal of Mathematics, 9(1), 237-244, (2020).
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2022-12-24
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