Remarks on almost η-Ricci solitons in (ε)-para Sasakian manifolds

Adara M. Blaga; Selcen Yüksel Perktaş

doi:10.31801/cfsuasmas.546595

Research Article

Remarks on almost η-Ricci solitons in (ε)-para Sasakian manifolds

Year 2019, Volume: 68 Issue: 2, 1621 - 1628, 01.08.2019

Adara M. Blaga Selcen Yüksel Perktaş

https://doi.org/10.31801/cfsuasmas.546595

Cited By: 12

Abstract

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.

Keywords

Almost η-Ricci solitons, (ε)-para Sasakian structure

References

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

Adara M. Blaga Selcen Yüksel Perktaş

https://doi.org/10.31801/cfsuasmas.546595

Cited By: 12

Abstract

References

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.

There are 10 citations in total.

Details

Primary Language	English
Journal Section	Review Articles
Authors	Adara M. Blaga 0000-0003-0237-3866 Selcen Yüksel Perktaş 0000-0002-8848-0621
Publication Date	August 1, 2019
Submission Date	March 27, 2018
Acceptance Date	February 5, 2019
Published in Issue	Year 2019 Volume: 68 Issue: 2

Cite

APA	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.