η-Ricci solitons in Kenmotsu manifolds

Baishya, Kanak Kanti; Chowdhury, Partha Roy

doi:10.2478/awutm-2019-0011

Abstract

The object of the present paper is to study generalized weakly symmetric and generalized weakly Ricci symmetric Kenmotsu manifolds whose metric tensor is η-Ricci soliton. The paper also aims to bring out curvature conditions for which η-Ricci solitons in Kenmotsu manifolds are sometimes shrinking or expanding and some other time remain steady. The existence of each generalized weakly symmetric and generalized weakly Ricci symmetric Kenmotsu manifold is ensured by an example.

References

[1] S. R. Ashoka, C. S. Bagewadi, and G. Ingalahalli, A Geometry on Ricci solitons in (LCS)_n-manifolds, Diff. Geom. Dynamical Systems, 16, (2014), 50-62
Search in Google Scholar Back to article
[2] C. S. Bagewadi and G. Ingalahalli, Ricci solitons in Lorentzian α-Sasakian manifolds, Acta Math. Academiae Paedagogicae Nyregyh aziensis, 28 (1), (2012), 59-6810.5402/2012/421384
Search in Google Scholar Back to article
[3] B. Barua and U. C. De, Characterizations of a Riemannian manifold admitting Ricci solitons, Facta Universitatis NIS, Ser. Math. Inform., 28 (2), (2013), 127-132
Search in Google Scholar Back to article
[4] K. K. Baishya and P. R. Chowdhury, η-Ricci solitons in (LCS)_n-manifolds, Bull. Transilv. Univ. Brasov, 9 (58) (2), (2016), 1-12
Search in Google Scholar Back to article
[5] K. K. Baishya and P. R. Chowdhury, Kenmotsu manifold with some curvature conditions, Annales Univ. Sci. Budapest. Eotvos Sect. Math., 59, (2016), 3-13
Search in Google Scholar Back to article
[6] K. K. Baishya, P. Peška, and P. R. Chowdhury, On almost generalized weakly symmetric Kenmotsu manifolds, Acta Univ. Palacki. Olomuc., Fac. rer. nat. Mathematica, 55 (2), (2016), 5-15
Search in Google Scholar Back to article
[7] K. K. Baishya, Note on almost generalized pseudo Ricci symmetric manifolds, Kyungpook Math.J., 57 (3), (2017), 517-523
Search in Google Scholar Back to article
[8] K. K. Baishya and P. R. Chowdhury, On almost generalized weakly symmetric LP-Sasakian manifold, An. Univ. Vest Timis. Ser. Mat.-Inform., 55 (2), (2017), 51-6410.1515/awutm-2017-0014
Search in Google Scholar Back to article
[9] K. K. Baishya, On generalized weakly symmetric manifolds, Bull. Transilv. Univ. Brasov, 10 (59), (2017), 31-38
Search in Google Scholar Back to article
[10] K. K. Baishya, On generalized semi-pseudo symmetric manifold, submitted
Search in Google Scholar Back to article
[11] C. L. Bejan and M. Crasmareanu, Ricci solitons in manifolds with quasi-constant curvature, Publ. Math. Debrecen, 78 (1), (2011), 235-24310.5486/PMD.2011.4797
Search in Google Scholar Back to article
[12] A. M. Blaga, Eta-Ricci solitons on para-Kenmotsu manifolds, Balkan J. Geom. Appl., 20 (1), (2015), 1-13
Search in Google Scholar Back to article
[13] A. M. Blaga, Eta-Ricci Solitons on Lorentzian Para-Sasakian Manifolds, Filomat, 30 (2), (2016), 489-49610.2298/FIL1602489B
Search in Google Scholar Back to article
[14] E. Cartan, Sur une classes remarquable d’espaces de Riemannian, Bull.Soc.Math. France, 54, (1926), 214-26410.24033/bsmf.1105
Search in Google Scholar Back to article
[15] M. C. Chaki, On pseudo symmetric manifolds, Analele Stiintifice ale Universitatii “Al I. Cuza” din Iasi, 33, (1987), 53-58
Search in Google Scholar Back to article
[16] M. C. Chaki and T. Kawaguchi, On almost pseudo Ricci symmetric manifolds, Tensor, 68 (1), (2007), 10-14
Search in Google Scholar Back to article
[17] U. C. De and S. Bandyopadhyay, On weakly symmetric spaces, Acta Mathematica Hungarica, 83, (2000), 205-21210.1023/A:1006759519940
Search in Google Scholar Back to article
[18] S. K. Dey and K. K. Baishya, Some results on Kenmotsu manifolds equipped with m-projective tensor, International J. of Math. Sci. and Engg. Appls., 8 (III), (2014), 205-214
Search in Google Scholar Back to article
[19] S. K. Dey and K. K. Baishya, On the existence of some types on Kenmotsu manifolds, Universal Journal of Mathematics and Mathematical Sciences, 3 (2), (2014), 13-32
Search in Google Scholar Back to article
[20] R. S. D. Dubey, Generalized recurrent spaces, Indian J. Pure Appl. Math., 10, (1979), 1508-1513
Search in Google Scholar Back to article
[21] S. K. Hui, A. A. Shaikh, and I. Roy, On totally umbilical hypersurfaces of weakly conharmonically symmetric spaces, Indian Journal of Pure and Applied Mathematics, 10 (4), (2010), 28-31
Search in Google Scholar Back to article
[22] A. Ghosh, R. Sharma, and J. T. Cho, Ann. Global Anal. Geom., 34 (3), (2008), 287-29510.1007/s10455-008-9112-1
Search in Google Scholar Back to article
[23] J. P. Jaiswal and R. H. Ojha, On weakly pseudo-projectively symmetric manifolds, Differential Geometry-Dynamical System, 12, (2010), 83-94
Search in Google Scholar Back to article
[24] D. Janssens and L. Vanhecke, Almost contact structures and curvature tensors, Kodai Math. J., 4, (1981), 1-2710.2996/kmj/1138036310
Search in Google Scholar Back to article
[25] J. B. June, U. C. De, and G. Pathak, On Kenmotsu manifolds, J. Korean Math. Soc., 42 (3), (2005), 435-44510.4134/JKMS.2005.42.3.435
Search in Google Scholar Back to article
[26] K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Mathematical Journal, 24 (1), (1972), 93-10310.2748/tmj/1178241594
Search in Google Scholar Back to article
[27] F. Malek and M. Samawaki, On weakly symmetric Riemannian manifolds, Differential Geometry-Dynamical System, 10, (2008), 215-220
Search in Google Scholar Back to article
[28] F.Özen and S. Altay, On weakly and pseudo symmetric Riemannian spaces, Indian Journal of Pure and Applied Mathematics, 33 (10), (2001), 1477-1488
Search in Google Scholar Back to article
[29] M. Prvanovic, On weakly symmetric Riemannian manifolds, Publicationes Mathematicae Debrecen, 46, (1995), 19-25
Search in Google Scholar Back to article
[30] M. Prvanovic, On totally umbilical submanifolds immersed in a weakly symmetric riemannian manifolds, Publicationes Mathematicae Debrecen, 6, (1998), 54-64
Search in Google Scholar Back to article
[31] A. A. Shaikh and K. K. Baishya, On weakly quasi-conformally symmetric manifolds, Soochow J. of Math., 31 (4), (2005), 581-595
Search in Google Scholar Back to article
[32] L. Tamássy andT.Q.Binh, On weakly symmetric and weakly projective symmetric Riemannian manifolds, Coll. Math. Soc. J. Bolyai, 56, (1989), 663-670
Search in Google Scholar Back to article
[33] M. Tarafdar and M. A. A. Jawarneh, Semi-Pseudo Ricci Symmetric manifold, J. Indian. Inst. of Science, 73, (1993), 591-596
Search in Google Scholar Back to article
[34] A. G. Walker, On Ruse’s space of recurrent curvature, Proc. of London Math. Soc., 52, (1950), 36-5410.1112/plms/s2-52.1.36
Search in Google Scholar Back to article

η-Ricci solitons in Kenmotsu manifolds

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