Yıl 2018, Cilt 47, Sayı 3, Sayfalar 579 - 587 2018-06-01

Ricci almost solitons on Concircular Ricci pseudosymmetric $\beta$-Kenmotsu manifolds

Shyamal Kumar Hui [1] , Debabrata Chakraborty [2]

47 70

The object of the present paper is to study concircular Ricci pseudosymmetric $\beta$-Kenmotsu manifolds whose metric is Ricci almost soliton. We found the conditions when Ricci almost soliton on concircular Ricci pseudosymmetric $\beta$-Kenmotsu manifold to be shrinking, steady and expanding respectively. We also construct an example of concircular Ricci pseudosymmetric $\beta$-Kenmotsu manifold whose metric is Ricci almost soliton.

Ricci almost soliton, $\beta$-Kenmotsu manifold, Ricci pseudosymmetric manifold, concircular curvature tensor
  • Ashoka, S. R., Bagewadi, C. S. and Ingalahalli, G., Certain results on Ricci solitons in - Sasakian manifolds, Hindawi Publ. Corporation, Geometry, Vol. 2013, Article ID 573925, 4 pages.
  • Ashoka, S. R., Bagewadi, C. S. and Ingalahalli, G., A geometry on Ricci solitons in (LCS)n- manifolds, Di. Geom.-Dynamical Systems, 16 (2014), 5062.
  • Bagewadi, C. S. and Ingalahalli, G., Ricci solitons in Lorentzian -Sasakian manifolds, Acta Math. Acad. Paeda. Nyire., 28 (2012), 5968.
  • Bejan, C. L. and Crasmareanu, M., Ricci solitons in manifolds with quasi constant curva- ture, Publ. Math. Debrecen, 78 (2011), 235243.
  • Blaga, A. M., $\eta$-Ricci solitons on para-kenmotsu manifolds, Balkan J. Geom. Appl., 20 (2015), 113.
  • Blair, D. E., Contact manifolds in Riemannian geometry, Lecture Notes in Math. 509, Springer-Verlag, 1976.
  • Calin, C. and Crasmareanu, M., From the Eisenhart problem to Ricci solitons in f- Kenmotsu manifolds, Bull. Malays. Math. Sci. Soc. (2), 33 (2010), 361368.
  • Chandra, S., Hui, S. K. and Shaikh, A. A., Second order parallel tensors and Ricci solitons on (LCS)n-manifolds, Commun. Korean Math. Soc., 30 (2015), 123130.
  • Chen, B. Y. and Deshmukh, S., Geometry of compact shrinking Ricci solitons, Balkan J. Geom. Appl., 19 (2014), 1321.
  • Deshmukh, S., Al-Sodais, H. and Alodan, H., A note on Ricci solitons, Balkan J. Geom. Appl.,16 (2011), 4855.
  • Deszcz, R., On Ricci-pseudosymmetric warped products, Demonstratio Math., 22 (1989), 10531065.
  • Deszcz R., On pseudosymmetric spaces, Bull. Soc. Math. Belg. Ser. A, 44(1) (1992), 134.
  • Hamilton, R. S., Three-manifolds with positive Ricci curvature, J. Di. Geom., 17 (1982), 255306.
  • Hamilton, R. S., The Ricci ow on surfaces, Mathematics and general relativity, Contemp. Math., 71, American Math. Soc., 1988, 237262.
  • Hui, S. K. and Chakraborty, D., Some types of Ricci solitons on (LCS)n-manifolds, J. Math. Sci. Advances and Applications, 37 (2016), 117.
  • Hui, S. K. and Chakraborty, D., Generalized Sasakian-space-forms and Ricci almost solitons with a conformal killing vector eld, New Trends in Math. Sci., 4 (2016), 263269.
  • Hui, S. K. and Lemence, R. S., Ricci pseudosymmetric generalized quasi-Einstein manifolds, SUT J. Math., 51 (2015), 6785.
  • Hui, S. K., Lemence, R. S. and Chakraborty, D., Ricci solitons on three dimensional gen- eralized Sasakian-space-forms, Tensor Society, N. S., 76 (2015), 75-83.
  • Ingalahalli, G. and Bagewadi, C. S., Ricci solitons in $\alpha$-Sasakian manifolds,Hindawi Pub- lishing Corporation, ISRN Geometry, Vol. 2012, Article ID 421384, 13 pages.
  • Jahanara, B., Haesen, S., Senturk, Z. and Verstraelen, L., On the parallel transport of the Ricci curvatures, J. Geom. Phys., 57 (2007), 17711777.
  • Kenmotsu, K., A class of almost contact Riemannian manifolds, Tohoku Math. J., 24 (1972), 93103.
  • Nagaraja, H. G. and Premalatha, C. R., Ricci solitons in Kenmotsu manifolds, J. Math. Analysis, 3 (2012), 1824.
  • Oubi~na, J. A., New classes of almost contact metric structures, Publ. Math. Debrecen, 32 (1985), 187193.
  • Perelman, G., The entropy formula for the Ricci ow and its geometric applications, http://arXiv.org/abs/math/0211159, 2002, 139.
  • Perelman, G., Ricci ow with surgery on three manifolds, http://arXiv.org/abs/math/0303109, 2003, 122.
  • Pigola, S., Rigoli, M., Rimoldi, M. and Setti, A. G., Ricci almost solitons, Ann. Sc. Norm. Super. Pisa Cl. Sci, 10 (2011), 757799.
  • Shaikh, A. A. and Hui, S. K., On some classes of generalized quasi-Einstein manifolds, Commun. Korean Math. Soc., 24(3) (2009), 415424.
  • Shaikh, A. A. and Hui, S. K., On locally $\phi$-symmetric $\beta$-kenmotsu manifolds, Extracta Mathematicae, 24(3) (2009), 301316.
  • Shaikh, A. A. and Hui, S. K., On extended generalized $\phi$-recurrent $\beta$-Kenmotsu Manifolds, Publ. de l'Institut Math. (Beograd), 89(103) (2011), 7788.
  • Sharma, R., Certain results on k-contact and (k,\mu)-contact manifolds, J. of Geom., 89 (2008), 138147.
  • Tripathi, M. M., Ricci solitons in contact metric manifolds, arxiv:0801.4221 [Math.DG] (2008).
  • Yano, K., Concircular geometry, I, Proc. Imp. Acad. Tokyo, 16 (1940), 195200.
Birincil Dil en
Konular Matematik
Dergi Bölümü Matematik
Yazarlar

Yazar: Shyamal Kumar Hui (Sorumlu Yazar)

Yazar: Debabrata Chakraborty

Bibtex @araştırma makalesi { hujms439993, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {Hacettepe Üniversitesi}, year = {2018}, volume = {47}, pages = {579 - 587}, doi = {}, title = {Ricci almost solitons on Concircular Ricci pseudosymmetric \$\\beta\$-Kenmotsu manifolds}, key = {cite}, author = {Hui, Shyamal Kumar and Chakraborty, Debabrata} }
APA Hui, S , Chakraborty, D . (2018). Ricci almost solitons on Concircular Ricci pseudosymmetric $\beta$-Kenmotsu manifolds. Hacettepe Journal of Mathematics and Statistics, 47 (3), 579-587. Retrieved from http://dergipark.gov.tr/hujms/issue/38121/439993
MLA Hui, S , Chakraborty, D . "Ricci almost solitons on Concircular Ricci pseudosymmetric $\beta$-Kenmotsu manifolds". Hacettepe Journal of Mathematics and Statistics 47 (2018): 579-587 <http://dergipark.gov.tr/hujms/issue/38121/439993>
Chicago Hui, S , Chakraborty, D . "Ricci almost solitons on Concircular Ricci pseudosymmetric $\beta$-Kenmotsu manifolds". Hacettepe Journal of Mathematics and Statistics 47 (2018): 579-587
RIS TY - JOUR T1 - Ricci almost solitons on Concircular Ricci pseudosymmetric $\beta$-Kenmotsu manifolds AU - Shyamal Kumar Hui , Debabrata Chakraborty Y1 - 2018 PY - 2018 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 579 EP - 587 VL - 47 IS - 3 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2017 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Ricci almost solitons on Concircular Ricci pseudosymmetric $\beta$-Kenmotsu manifolds %A Shyamal Kumar Hui , Debabrata Chakraborty %T Ricci almost solitons on Concircular Ricci pseudosymmetric $\beta$-Kenmotsu manifolds %D 2018 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 47 %N 3 %R %U
ISNAD Hui, Shyamal Kumar , Chakraborty, Debabrata . "Ricci almost solitons on Concircular Ricci pseudosymmetric $\beta$-Kenmotsu manifolds". Hacettepe Journal of Mathematics and Statistics 47 / 3 (Haziran 2018): 579-587.