We consider almost η-Ricci solitons in (ε)-para Sasakian manifolds satisfying certain curvature conditions. In the gradient case we give an estimation for the norm of the Ricci curvature tensor and express the scalar curvature of the manifold in terms of the two functions that define the soliton. We also prove that if the Ricci operator is of Codazzi type, then the gradient η-Ricci soliton is expanding if M is spacelike or shrinking if M is timelike.
Acet, B. E., A note on Ricci solitons on para-Sasakian manifolds, J. Sci. Tech., 11, (2018), no. 2, 237--242.
Blaga, A. M., Almost η-Ricci solitons in (LCS)_{n}-manifolds, to appear in Bull. Belg. Math. Soc. Simon Stevin, 25, (2018), no 5, 641--653
Blaga, A. M., η-Ricci solitons on Lorentzian para-Sasakian manifolds, Filomat, 30, (2016), no. 2, 489--496.
Blaga, A. M., Perktaş, S. Y., Acet, B. E., Erdoğan, F. E., η-Ricci solitons in (ε)-almost paracontact metric manifolds, Glasnik Matematicki, 53, (2018), no. 1, 377--410.
Cho, J. T., Kimura, M., Ricci solitons and real hypersurfaces in a complex space form, Tôhoku Math. J., 61, (2009), no. 2, 205--212.
Crasmareanu, M., A new approach to gradient Ricci solitons and generalizations, to appear in Filomat.
Hamilton, R. S., Three-manifolds with positive Ricci curvature, J. Diff. Geom., 17, (1982), 255--306.
Pigola, S., Rigoli, M., Rimoldi, M., Setti, A., Ricci almost solitons, Ann. Sc. Norm. Super. Pisa Cl. Sci., (5) 10, (2011), 757--799.
Satō, I., On a structure similar to the almost contact structure, Tensor (N.S.), 30, (1976), no. 3, 219--224.
Tripathi, M. M., Kılıç, E., Perktaş, S. Y., Keleş, S., Indefinite almost paracontact metric manifolds, Int. J. Math. Math. Sci., (2010), 846195, pp. 19.
Year 2019,
Volume: 68 Issue: 2, 1621 - 1628, 01.08.2019
Acet, B. E., A note on Ricci solitons on para-Sasakian manifolds, J. Sci. Tech., 11, (2018), no. 2, 237--242.
Blaga, A. M., Almost η-Ricci solitons in (LCS)_{n}-manifolds, to appear in Bull. Belg. Math. Soc. Simon Stevin, 25, (2018), no 5, 641--653
Blaga, A. M., η-Ricci solitons on Lorentzian para-Sasakian manifolds, Filomat, 30, (2016), no. 2, 489--496.
Blaga, A. M., Perktaş, S. Y., Acet, B. E., Erdoğan, F. E., η-Ricci solitons in (ε)-almost paracontact metric manifolds, Glasnik Matematicki, 53, (2018), no. 1, 377--410.
Cho, J. T., Kimura, M., Ricci solitons and real hypersurfaces in a complex space form, Tôhoku Math. J., 61, (2009), no. 2, 205--212.
Crasmareanu, M., A new approach to gradient Ricci solitons and generalizations, to appear in Filomat.
Hamilton, R. S., Three-manifolds with positive Ricci curvature, J. Diff. Geom., 17, (1982), 255--306.
Pigola, S., Rigoli, M., Rimoldi, M., Setti, A., Ricci almost solitons, Ann. Sc. Norm. Super. Pisa Cl. Sci., (5) 10, (2011), 757--799.
Satō, I., On a structure similar to the almost contact structure, Tensor (N.S.), 30, (1976), no. 3, 219--224.
Tripathi, M. M., Kılıç, E., Perktaş, S. Y., Keleş, S., Indefinite almost paracontact metric manifolds, Int. J. Math. Math. Sci., (2010), 846195, pp. 19.
Blaga, A. M., & Perktaş, S. Y. (2019). Remarks on almost η-Ricci solitons in (ε)-para Sasakian manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1621-1628. https://doi.org/10.31801/cfsuasmas.546595
AMA
Blaga AM, Perktaş SY. Remarks on almost η-Ricci solitons in (ε)-para Sasakian manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1621-1628. doi:10.31801/cfsuasmas.546595
Chicago
Blaga, Adara M., and Selcen Yüksel Perktaş. “Remarks on Almost η-Ricci Solitons in (ε)-Para Sasakian Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1621-28. https://doi.org/10.31801/cfsuasmas.546595.
EndNote
Blaga AM, Perktaş SY (August 1, 2019) Remarks on almost η-Ricci solitons in (ε)-para Sasakian manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1621–1628.
IEEE
A. M. Blaga and S. Y. Perktaş, “Remarks on almost η-Ricci solitons in (ε)-para Sasakian manifolds”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1621–1628, 2019, doi: 10.31801/cfsuasmas.546595.
ISNAD
Blaga, Adara M. - Perktaş, Selcen Yüksel. “Remarks on Almost η-Ricci Solitons in (ε)-Para Sasakian Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1621-1628. https://doi.org/10.31801/cfsuasmas.546595.
JAMA
Blaga AM, Perktaş SY. Remarks on almost η-Ricci solitons in (ε)-para Sasakian manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1621–1628.
MLA
Blaga, Adara M. and Selcen Yüksel Perktaş. “Remarks on Almost η-Ricci Solitons in (ε)-Para Sasakian Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1621-8, doi:10.31801/cfsuasmas.546595.
Vancouver
Blaga AM, Perktaş SY. Remarks on almost η-Ricci solitons in (ε)-para Sasakian manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1621-8.