Yamabe solitons on some types of generalized Sasakian space forms
DOI:
https://doi.org/10.5269/bspm.47828Abstract
The object of the present paper is to study Yamabe solitons on three dimensional generalized Sasakian space forms with quasi-Sasakian mertic and Kenmotsu metric. Illustrative examples have been given.
References
1. Alegre, P. and Carriazo, A., Structures on generalized Sasakian space forms, Differential Geom. Appl., 26(2008), 656-666. https://doi.org/10.1016/j.difgeo.2008.04.014
2. Aubin, T., Equations differentielles non-lineaires et probleme de Yamabe concernant la courbure scalaire, J. Math. Pure Appl., 55(1976), 269-296.
3. De, U. C. and Sarkar, A., On projective curvature tensor of generalized Sasakian space forms, Quaest Math., 33(2010), 245-252. https://doi.org/10.2989/16073606.2010.491203
4. De, U. C. and Sarkar, A., Some results on Generalized Sasakian space forms, Thai J. of Math., 8(2010), 1-10.
5. Deshmukh, S. and Chen, B. Y., A note on Yamabe solitons, Balkan J. Geom. and Appl., 23(2018), 37-43.
6. Hamilton, R. S., The Ricci flow on surfaces, Mathematics and general Relativity, Contemp. Math., 71(1988), 237-262. https://doi.org/10.1090/conm/071/954419
7. Hui, S. K. and Sarkar, A., On W2 curvature tensor of generalized Sasakian space form, Math. Panonica, 23(2012), 113-124.
8. Kundu, S., On Yamabe soliton, Irish Mathematical Society Bulletin, 77(2016), 51-60. https://doi.org/10.33232/BIMS.0077.51.60
9. Sarkar, A. and De, U. C., Some curvature properties of generalized Sasakian space forms, Lobachevskii J. Math., 33(2012), 22-27. https://doi.org/10.1134/S1995080212010088
10. Sarkar, A. and Sen, M., Locally φ-symmetric generalized Sasakian space forms, Ukrainian Math. J., 65(2014), 1588-1597. https://doi.org/10.1007/s11253-014-0881-3
11. Sarkar, A. and Sen, M., On φ-recurrent generalized Sasakian space forms, Lobachevskii J. Math., 33(2012), 244-248. https://doi.org/10.1134/S1995080212030146
12. Schoen, R., Conformal deformation of a Riemannian metric to constant scalar curvature, J. Diff. Geom., 20(1984), 479-495. https://doi.org/10.4310/jdg/1214439291
13. Sharma, R., A 3-dimensional Sasakian metric as a Yamabe soliton, Int. J. Geom. Methods in Mod. Phys., 09(2012), 1220003, 5pp. https://doi.org/10.1142/S0219887812200034
14. Trudinger, S. N., Remarks on the deformation of Riemannian structure on compact manifolds, Ann. Scu. Norm. Sup. Pisa, 22(1968), 265-274.
15. Yamabe, H., On a deformation of Riemannian structures on compact manifolds, Osaka Math. J., 12(1960), 21-37.
16. Yano, K., Integrals formulas on Riemannian geometry, Marcel Dekker, 1970.
2. Aubin, T., Equations differentielles non-lineaires et probleme de Yamabe concernant la courbure scalaire, J. Math. Pure Appl., 55(1976), 269-296.
3. De, U. C. and Sarkar, A., On projective curvature tensor of generalized Sasakian space forms, Quaest Math., 33(2010), 245-252. https://doi.org/10.2989/16073606.2010.491203
4. De, U. C. and Sarkar, A., Some results on Generalized Sasakian space forms, Thai J. of Math., 8(2010), 1-10.
5. Deshmukh, S. and Chen, B. Y., A note on Yamabe solitons, Balkan J. Geom. and Appl., 23(2018), 37-43.
6. Hamilton, R. S., The Ricci flow on surfaces, Mathematics and general Relativity, Contemp. Math., 71(1988), 237-262. https://doi.org/10.1090/conm/071/954419
7. Hui, S. K. and Sarkar, A., On W2 curvature tensor of generalized Sasakian space form, Math. Panonica, 23(2012), 113-124.
8. Kundu, S., On Yamabe soliton, Irish Mathematical Society Bulletin, 77(2016), 51-60. https://doi.org/10.33232/BIMS.0077.51.60
9. Sarkar, A. and De, U. C., Some curvature properties of generalized Sasakian space forms, Lobachevskii J. Math., 33(2012), 22-27. https://doi.org/10.1134/S1995080212010088
10. Sarkar, A. and Sen, M., Locally φ-symmetric generalized Sasakian space forms, Ukrainian Math. J., 65(2014), 1588-1597. https://doi.org/10.1007/s11253-014-0881-3
11. Sarkar, A. and Sen, M., On φ-recurrent generalized Sasakian space forms, Lobachevskii J. Math., 33(2012), 244-248. https://doi.org/10.1134/S1995080212030146
12. Schoen, R., Conformal deformation of a Riemannian metric to constant scalar curvature, J. Diff. Geom., 20(1984), 479-495. https://doi.org/10.4310/jdg/1214439291
13. Sharma, R., A 3-dimensional Sasakian metric as a Yamabe soliton, Int. J. Geom. Methods in Mod. Phys., 09(2012), 1220003, 5pp. https://doi.org/10.1142/S0219887812200034
14. Trudinger, S. N., Remarks on the deformation of Riemannian structure on compact manifolds, Ann. Scu. Norm. Sup. Pisa, 22(1968), 265-274.
15. Yamabe, H., On a deformation of Riemannian structures on compact manifolds, Osaka Math. J., 12(1960), 21-37.
16. Yano, K., Integrals formulas on Riemannian geometry, Marcel Dekker, 1970.
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2022-01-26
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University Grants Commission
Grant numbers 423044
