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Journals / International Electronic Journal of Geometry / 2021 / Cilt: 14 - Sayı: 1

A Note on Gradient Solitons in Three-Dimensional Riemannian Manifolds

Uday CHAND DE
Fatemah MOFARREH
Pages
85–90
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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

We charecterize three-dimensional Riemannian manifolds endowed with a special type of vector field if the Riemannian metrices are gradient Yamabe solitons and gradient Einstein solitons respectively.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We charecterize three-dimensional Riemannian manifolds endowed with a special type of vector field if the Riemannian metrices are gradient Yamabe solitons and gradient Einstein solitons respectively.
📊
Key Findings & Data:We charecterize three-dimensional Riemannian manifolds endowed with a special type of vector field if the Riemannian metrices are gradient Yamabe solitons and gradient Einstein solitons respectively.
💡
Conclusion & Impact:We charecterize three-dimensional Riemannian manifolds endowed with a special type of vector field if the Riemannian metrices are gradient Yamabe solitons and gradient Einstein solitons respectively.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Gradient Yamabe soliton · gradient Einstein soliton · Riemannian manifold

Abstract

We charecterize three-dimensional Riemannian manifolds endowed with a special type of vector field if the Riemannian metrices are gradient Yamabe solitons and gradient Einstein solitons respectively.

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Cite This Article

DE, U. C., MOFARREH, F. (2022). A Note on Gradient Solitons in Three-Dimensional Riemannian Manifolds. International Electronic Journal of Geometry, Cilt: 14 - Sayı: 1, 85–90. https://ajindex.com/articles/539587

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References (19)

  1. Blaga, A. M.: On gradient eta-Einstein solitons. Kragujevac Journal of Mathematics. 42, 229-237 (2018)
  2. Blaga, A. M.: Some geometrical aspects of Einstein, Ricci and Yamabe solitons. J. Geom. Sym. Physics. 52, 17-26 (2019)
  3. Blaga, A. M. and Ozgur, C.: Almost eta-Ricci and almost eta-Yamabe solitons with torse-forming potential vector field. Quaestiones Mathematicae.
  4. Cao, H. D., Sun, X. F. and Zhang, Y. Y.: On the structure of gradient Yamabe solitons. Mathematical Research Letters. 19, 737-774 (2002)
  5. Catino, G., Mazzieri, L.: Gradient Einstein soliton. Nonlinear Anal., 132, 66-94 (2016)
  6. Chen, B.Y. and Deshmukh S.: Yamabe and quasi-Yamabe solitons on Euclidean submanifolds. Mediterr. J. Math. 15, 194 (2018)
  7. De, U.C., Chaubey, S.K. and Suh, Y.J.: A note on almost co-Kahler manifolds. Int. J. of Geo. Methods in Modern Phy. 17 (10), 2050153 (2020)
  8. Desmukh, S. and Chen, B. Y.: A note on Yamabe solitons. Balk. J. Geo. Appl. 23, 37-43 (2018)
  9. Hamilton, R.S.: The Ricci flow on surfaces. Mathematics and general Relativity, Contemp. Math. 71, 237-262(1998)
  10. Hsu, S.Y.: A note on compact gradient Yamabe solitons. J. Math. Ana. Appl. 388, 725-726 (2012)
  11. Karaca, F.: Gradient Yamabe solitons on Multiply Warped product Manifolds. Int. Electronic J. Geom. 12, 157-168 (2019)
  12. Karatsobanis, J. N. and Xenos, P. J.: On the new class of contact metric 3-manifolds. J. Geom. 80, 136-153 (2004)
  13. Koufogiorgos, T.: On a class of contact Riemannian 3-manifolds. Results in Math. 27, 51-62 (1995)
  14. Kowalski, O.: An explicit classification of 3-dimensional Riemannian spaces satisfying R(X; Y ):R = 0. Czechoslovak Math. J. 46(121), 427-474 (1996)
  15. Suh, Y.J. and De, U.C.: Yamabe solitons and gradient Yamabe solitons on three-dimensional N(k)-contact manifolds. Int. J. Geom. Methods Mod. Phys. 17 (12) 2050177, 10 pp. (2020)
  16. Thurston, W. P. and Winkelnkemper, H. E.: On the existence of contact forms. Proc. Amer. Math. Soc. 52, 345-347 (1975)
  17. Trudinger, N. S.: Remarks concerning the conformal deformation of Riemannian structures on compact manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 3. 22, 265-274 (1968)
  18. Wang, Y.: Yamabe soliton on 3-dimensional Kenmotsu manifolds. Bull. Belg. Math. Soc. Simon Stevin. 23, 345-355 (2016)
  19. Yamabe, H.: On a deformation of Riemannian structures on compact manifolds. Osaka Math. J. 12 21