1. bookVolume 57 (2019): Issue 2 (December 2019)
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22 Nov 2012
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access type Open Access

η-Ricci solitons in Kenmotsu manifolds

Published Online: 21 Dec 2020
Page range: 1 - 17
Journal Details
License
Format
Journal
First Published
22 Nov 2012
Publication timeframe
2 times per year
Languages
English
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.

Keywords

[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

[2] C. S. Bagewadi and G. Ingalahalli, Ricci solitons in Lorentzian α-Sasakian manifolds, Acta Math. Academiae Paedagogicae Nyregyh aziensis, 28 (1), (2012), 59-68 Search in Google Scholar

[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

[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

[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

[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

[7] K. K. Baishya, Note on almost generalized pseudo Ricci symmetric manifolds, Kyungpook Math.J., 57 (3), (2017), 517-523 Search in Google Scholar

[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), 51-64 Search in Google Scholar

[9] K. K. Baishya, On generalized weakly symmetric manifolds, Bull. Transilv. Univ. Brasov, 10 (59), (2017), 31-38 Search in Google Scholar

[10] K. K. Baishya, On generalized semi-pseudo symmetric manifold, submitted Search in Google Scholar

[11] C. L. Bejan and M. Crasmareanu, Ricci solitons in manifolds with quasi-constant curvature, Publ. Math. Debrecen, 78 (1), (2011), 235-243 Search in Google Scholar

[12] A. M. Blaga, Eta-Ricci solitons on para-Kenmotsu manifolds, Balkan J. Geom. Appl., 20 (1), (2015), 1-13 Search in Google Scholar

[13] A. M. Blaga, Eta-Ricci Solitons on Lorentzian Para-Sasakian Manifolds, Filomat, 30 (2), (2016), 489-496 Search in Google Scholar

[14] E. Cartan, Sur une classes remarquable d’espaces de Riemannian, Bull.Soc.Math. France, 54, (1926), 214-264 Search in Google Scholar

[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

[16] M. C. Chaki and T. Kawaguchi, On almost pseudo Ricci symmetric manifolds, Tensor, 68 (1), (2007), 10-14 Search in Google Scholar

[17] U. C. De and S. Bandyopadhyay, On weakly symmetric spaces, Acta Mathematica Hungarica, 83, (2000), 205-212 Search in Google Scholar

[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

[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

[20] R. S. D. Dubey, Generalized recurrent spaces, Indian J. Pure Appl. Math., 10, (1979), 1508-1513 Search in Google Scholar

[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

[22] A. Ghosh, R. Sharma, and J. T. Cho, Ann. Global Anal. Geom., 34 (3), (2008), 287-295 Search in Google Scholar

[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

[24] D. Janssens and L. Vanhecke, Almost contact structures and curvature tensors, Kodai Math. J., 4, (1981), 1-27 Search in Google Scholar

[25] J. B. June, U. C. De, and G. Pathak, On Kenmotsu manifolds, J. Korean Math. Soc., 42 (3), (2005), 435-445 Search in Google Scholar

[26] K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Mathematical Journal, 24 (1), (1972), 93-103 Search in Google Scholar

[27] F. Malek and M. Samawaki, On weakly symmetric Riemannian manifolds, Differential Geometry-Dynamical System, 10, (2008), 215-220 Search in Google Scholar

[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

[29] M. Prvanovic, On weakly symmetric Riemannian manifolds, Publicationes Mathematicae Debrecen, 46, (1995), 19-25 Search in Google Scholar

[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

[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

[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

[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

[34] A. G. Walker, On Ruse’s space of recurrent curvature, Proc. of London Math. Soc., 52, (1950), 36-54 Search in Google Scholar

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