SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2019 / Volume: 68 Issue: 2

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

Adara M. Blaga0000-0003-0237-3866
Selcen Yüksel Perktaş0000-0002-8848-0621
Pages
—
Publication Date
2019-08-01
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We consider almost η-Ricci solitons in (ε)-para Sasakian manifolds satisfying certain curvature conditions.
📊
Key Findings & Data: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.
💡
Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Almost η-Ricci solitons · (ε)-para Sasakian structure

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.

🔖

Cite This Article

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, Volume: 68 Issue: 2. https://doi.org/10.31801/cfsuasmas.546595

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (10)

  1. Acet, B. E., A note on Ricci solitons on para-Sasakian manifolds, J. Sci. Tech., 11, (2018), no. 2, 237--242.
  2. 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
  3. Blaga, A. M., η-Ricci solitons on Lorentzian para-Sasakian manifolds, Filomat, 30, (2016), no. 2, 489--496.
  4. 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.
  5. Cho, J. T., Kimura, M., Ricci solitons and real hypersurfaces in a complex space form, Tôhoku Math. J., 61, (2009), no. 2, 205--212.
  6. Crasmareanu, M., A new approach to gradient Ricci solitons and generalizations, to appear in Filomat.
  7. Hamilton, R. S., Three-manifolds with positive Ricci curvature, J. Diff. Geom., 17, (1982), 255--306.
  8. Pigola, S., Rigoli, M., Rimoldi, M., Setti, A., Ricci almost solitons, Ann. Sc. Norm. Super. Pisa Cl. Sci., (5) 10, (2011), 757--799.
  9. Satō, I., On a structure similar to the almost contact structure, Tensor (N.S.), 30, (1976), no. 3, 219--224.
  10. Tripathi, M. M., Kılıç, E., Perktaş, S. Y., Keleş, S., Indefinite almost paracontact metric manifolds, Int. J. Math. Math. Sci., (2010), 846195, pp. 19.